{
  "paper": {
    "school": "Rosyth",
    "year": 2024,
    "level": "P5",
    "label": "Weighted Assessment 2",
    "source_prefix": "Rosyth 2024 P5 Weighted Assessment 2",
    "has_answer_key": true
  },
  "questions": [
    {
      "n": 1,
      "type_id": 1,
      "question": "Find the missing number in the box.<br>$$280 \\times 500 = \\boxed{?}$$",
      "answer0": "1400",
      "answer1": "14 000",
      "answer2": "140 000",
      "answer3": "1 400 000",
      "correct_answer": 2,
      "skill_id": 151,
      "difficulty_id": 1,
      "explanation": "Method: multiply by tens and hundreds. \\(280 \\times 500 = 280 \\times 5 \\times 100 = 1400 \\times 100 = 140\\,000\\). Answer: 140 000.",
      "hints": ["Break 500 into \\(5 \\times 100\\).", "First find \\(280 \\times 5 = 1400\\), then multiply by 100."],
      "source": "Rosyth 2024 P5 Weighted Assessment 2 Q1",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "notes": "Answer key: option 3 (140 000)."
    },
    {
      "n": 2,
      "type_id": 1,
      "question": "In a box of apples, 8 of them are red and 12 of them are green. Express the ratio of the number of red apples to the total number of apples in its simplest form.",
      "answer0": "2 : 3",
      "answer1": "2 : 5",
      "answer2": "3 : 2",
      "answer3": "3 : 5",
      "correct_answer": 1,
      "skill_id": 179,
      "difficulty_id": 1,
      "explanation": "Method: form the ratio then simplify. Total apples \\(= 8 + 12 = 20\\). Red : total \\(= 8 : 20 = 2 : 5\\). Answer: 2 : 5.",
      "hints": ["Total apples = red + green = 8 + 12.", "Divide both numbers of \\(8 : 20\\) by 4."],
      "source": "Rosyth 2024 P5 Weighted Assessment 2 Q2",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "notes": "Ratio answer so MCQ. Answer key: option 2 (2 : 5)."
    },
    {
      "n": 3,
      "type_id": 1,
      "question": "In Triangle XYZ, the base is XY. Name its height.",
      "answer0": "WZ",
      "answer1": "VX",
      "answer2": "XZ",
      "answer3": "YZ",
      "correct_answer": 1,
      "skill_id": 185,
      "difficulty_id": 2,
      "explanation": "Method: the height is the perpendicular from the opposite vertex Z to the base line XY. The segment VX is drawn perpendicular to XY (shown by the right-angle mark at V) from vertex Z's line, so the height of the triangle relative to base XY is VX. Answer: VX.",
      "hints": ["The height is perpendicular to the chosen base.", "Look for the segment that meets base XY at a right angle."],
      "source": "Rosyth 2024 P5 Weighted Assessment 2 Q3",
      "image_needed": true,
      "image_options": false,
      "image_file": "q3.png",
      "image_page": 3,
      "image_bbox": [0.18, 0.62, 0.62, 0.80],
      "notes": "Diagram: triangle XYZ with perpendicular VX marked. Answer key: option 1 (VX)."
    },
    {
      "n": 4,
      "type_id": 1,
      "question": "ABCD is a square of side 10 cm. Find the area of the shaded triangle.",
      "answer0": "15 cm²",
      "answer1": "30 cm²",
      "answer2": "35 cm²",
      "answer3": "70 cm²",
      "correct_answer": 2,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Method: area of triangle \\(= \\dfrac{1}{2} \\times \\text{base} \\times \\text{height}\\). The shaded triangle has its base along DC (the full side = 10 cm) and the apex at the midpoint on AD, giving height = 7 cm (10 cm side minus the 3 cm marked at the top). Area \\(= \\dfrac{1}{2} \\times 10 \\times 7 = 35\\) cm². Answer: 35 cm².",
      "hints": ["Area of a triangle \\(= \\dfrac{1}{2} \\times \\text{base} \\times \\text{height}\\).", "The base is the 10 cm side; the height is \\(10 - 3 = 7\\) cm."],
      "source": "Rosyth 2024 P5 Weighted Assessment 2 Q4",
      "image_needed": true,
      "image_options": false,
      "image_file": "q4.png",
      "image_page": 4,
      "image_bbox": [0.20, 0.14, 0.48, 0.31],
      "notes": "Square ABCD side 10 cm, 3 cm marked from B downward; shaded triangle apex on left side. Answer key: option 3 (35 cm²)."
    },
    {
      "n": 5,
      "type_id": 1,
      "question": "A bottle contained \\(\\dfrac{8}{9}\\) \\(\\ell\\) of milk. Wilson drank \\(\\dfrac{3}{4}\\) \\(\\ell\\) of it. How much milk was left in the bottle?",
      "answer0": "\\(\\dfrac{1}{4}\\) \\(\\ell\\)",
      "answer1": "\\(\\dfrac{2}{9}\\) \\(\\ell\\)",
      "answer2": "\\(\\dfrac{2}{3}\\) \\(\\ell\\)",
      "answer3": "\\(\\dfrac{5}{36}\\) \\(\\ell\\)",
      "correct_answer": 3,
      "skill_id": 159,
      "difficulty_id": 2,
      "explanation": "Method: subtract the fractions using a common denominator. \\(\\dfrac{8}{9} - \\dfrac{3}{4} = \\dfrac{32}{36} - \\dfrac{27}{36} = \\dfrac{5}{36}\\). Answer: \\(\\dfrac{5}{36}\\) \\(\\ell\\).",
      "hints": ["Use a common denominator of 36.", "\\(\\dfrac{8}{9} = \\dfrac{32}{36}\\) and \\(\\dfrac{3}{4} = \\dfrac{27}{36}\\)."],
      "source": "Rosyth 2024 P5 Weighted Assessment 2 Q5",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "notes": "Fraction answer so MCQ. Answer key: option 4 (5/36)."
    },
    {
      "n": 6,
      "type_id": 2,
      "question": "Find the value of \\(24 + 6 \\times (13 - 9) \\div 3\\).<br>[?]",
      "answer0": "32",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 155,
      "difficulty_id": 2,
      "explanation": "Method: order of operations (brackets, then × and ÷ left to right, then +). \\(13 - 9 = 4\\); \\(6 \\times 4 = 24\\); \\(24 \\div 3 = 8\\); \\(24 + 8 = 32\\). Answer: 32.",
      "hints": ["Work out the brackets first: \\(13 - 9\\).", "Do multiplication and division before addition."],
      "source": "Rosyth 2024 P5 Weighted Assessment 2 Q6",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "notes": "Answer key: 24 + 6 x 4 ÷ 3 = 32."
    },
    {
      "n": 7,
      "type_id": 2,
      "question": "Find the missing number in the box.<br>\\([?] : 4 = 15 : 20\\)",
      "answer0": "3",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 181,
      "difficulty_id": 1,
      "explanation": "Method: find the missing term in equivalent ratios. \\(20 \\div 4 = 5\\), so divide 15 by 5: \\(15 \\div 5 = 3\\). The missing number is 3. Check: \\(3 : 4 = 15 : 20\\). Answer: 3.",
      "hints": ["20 is 4 multiplied by 5, so the second ratio is 5 times the first.", "Divide 15 by 5 to find the missing term."],
      "source": "Rosyth 2024 P5 Weighted Assessment 2 Q7",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "notes": "Answer key: 3."
    },
    {
      "n": 8,
      "type_id": 1,
      "question": "Arrange the following fractions from the smallest to the greatest.<br>\\(\\dfrac{5}{7}\\), \\(\\dfrac{4}{9}\\), \\(\\dfrac{1}{2}\\)",
      "answer0": "\\(\\dfrac{4}{9}\\), \\(\\dfrac{1}{2}\\), \\(\\dfrac{5}{7}\\)",
      "answer1": "\\(\\dfrac{1}{2}\\), \\(\\dfrac{4}{9}\\), \\(\\dfrac{5}{7}\\)",
      "answer2": "\\(\\dfrac{5}{7}\\), \\(\\dfrac{1}{2}\\), \\(\\dfrac{4}{9}\\)",
      "answer3": "\\(\\dfrac{4}{9}\\), \\(\\dfrac{5}{7}\\), \\(\\dfrac{1}{2}\\)",
      "correct_answer": 0,
      "skill_id": 158,
      "difficulty_id": 2,
      "explanation": "Method: convert to decimals (or a common denominator) to compare. \\(\\dfrac{4}{9} \\approx 0.44\\), \\(\\dfrac{1}{2} = 0.5\\), \\(\\dfrac{5}{7} \\approx 0.71\\). Smallest to greatest: \\(\\dfrac{4}{9}\\), \\(\\dfrac{1}{2}\\), \\(\\dfrac{5}{7}\\).",
      "hints": ["Convert each fraction to a decimal to compare them.", "\\(\\dfrac{4}{9} \\approx 0.44\\), \\(\\dfrac{1}{2} = 0.5\\), \\(\\dfrac{5}{7} \\approx 0.71\\)."],
      "source": "Rosyth 2024 P5 Weighted Assessment 2 Q8",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "notes": "Ordering of fractions; rendered as MCQ since answer values are fractions (cannot be FIB). Answer key order: 4/9, 1/2, 5/7."
    },
    {
      "n": 9,
      "type_id": 2,
      "question": "Rectangle ABCD is made up of 5 identical rectangles. Find the area of the shaded triangle.<br>[?] cm²",
      "answer0": "24",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 2,
      "explanation": "Method: area of triangle \\(= \\dfrac{1}{2} \\times \\text{base} \\times \\text{height}\\). The shaded triangle has base along the top (2 small rectangles = \\(2 \\times 3 = 6\\) cm) and height = 8 cm. Area \\(= \\dfrac{1}{2} \\times 6 \\times 8 = 24\\) cm². Answer: 24 cm².",
      "hints": ["Each small rectangle is 3 cm wide; the triangle base spans 2 of them.", "Area of triangle \\(= \\dfrac{1}{2} \\times \\text{base} \\times \\text{height}\\)."],
      "source": "Rosyth 2024 P5 Weighted Assessment 2 Q9",
      "image_needed": true,
      "image_options": false,
      "image_file": "q9.png",
      "image_page": 7,
      "image_bbox": [0.16, 0.14, 0.58, 0.31],
      "notes": "Rectangle ABCD split into 5 identical 3 cm strips, height 8 cm; shaded triangle. Answer key: 1/2 x 6 x 8 = 24 cm²."
    },
    {
      "n": 10,
      "type_id": 2,
      "question": "The lengths of three ribbons are in the ratio 2 : 3 : 4. The total length of the three ribbons is 126 cm. What is the length of the shortest ribbon?<br>[?] cm",
      "answer0": "28",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 2,
      "explanation": "Method: divide the total by the number of units, then find the shortest. Total units \\(= 2 + 3 + 4 = 9\\). \\(126 \\div 9 = 14\\) cm per unit. Shortest ribbon \\(= 2 \\times 14 = 28\\) cm. Answer: 28 cm.",
      "hints": ["Add the ratio parts: \\(2 + 3 + 4\\).", "Find the value of 1 unit, then multiply by 2 for the shortest."],
      "source": "Rosyth 2024 P5 Weighted Assessment 2 Q10",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "notes": "Answer key: 4+3+2=9, 126÷9=14, 14x2=28 cm."
    },
    {
      "n": 11,
      "type_id": 1,
      "question": "Find the product of \\(\\dfrac{5}{6}\\) and \\(\\dfrac{8}{5}\\). Express your answer as a mixed number in its simplest form.",
      "answer0": "\\(1\\dfrac{1}{3}\\)",
      "answer1": "\\(1\\dfrac{1}{6}\\)",
      "answer2": "\\(\\dfrac{4}{3}\\)",
      "answer3": "\\(1\\dfrac{3}{10}\\)",
      "correct_answer": 0,
      "skill_id": 162,
      "difficulty_id": 2,
      "explanation": "Method: multiply the fractions then convert to a mixed number. \\(\\dfrac{5}{6} \\times \\dfrac{8}{5} = \\dfrac{40}{30} = \\dfrac{4}{3} = 1\\dfrac{1}{3}\\). Answer: \\(1\\dfrac{1}{3}\\).",
      "hints": ["Multiply numerators and denominators, then simplify.", "\\(\\dfrac{4}{3}\\) as a mixed number is \\(1\\dfrac{1}{3}\\)."],
      "source": "Rosyth 2024 P5 Weighted Assessment 2 Q11",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "notes": "Mixed-number answer so MCQ. Answer key: 5/6 x 8/5 = 4/3 = 1 1/3."
    },
    {
      "n": 12,
      "type_id": 2,
      "question": "Ali bought some cookies. He ate \\(\\dfrac{1}{4}\\) of them on Monday and \\(\\dfrac{1}{6}\\) of them on Tuesday. He ate 9 more cookies on Monday than on Tuesday. How many cookies did Ali buy altogether?<br>[?]",
      "answer0": "108",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 2,
      "explanation": "Method: find the fraction difference, then the whole. \\(\\dfrac{1}{4} = \\dfrac{6}{24}\\) and \\(\\dfrac{1}{6} = \\dfrac{4}{24}\\). Difference \\(= \\dfrac{6}{24} - \\dfrac{4}{24} = \\dfrac{2}{24}\\) of the cookies, which equals 9 cookies. So \\(\\dfrac{2}{24}\\) = 9 means \\(\\dfrac{1}{24} = 4.5\\), and the whole \\(= 4.5 \\times 24 = 108\\). Answer: 108 cookies.",
      "hints": ["Express \\(\\dfrac{1}{4}\\) and \\(\\dfrac{1}{6}\\) over a common denominator of 24.", "The difference \\(\\dfrac{2}{24}\\) of the total equals 9 cookies."],
      "source": "Rosyth 2024 P5 Weighted Assessment 2 Q12",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "notes": "Answer key: 1/4=6/24, 1/6=4/24, 9÷2=4.5, 4.5x24=108."
    },
    {
      "n": 13,
      "type_id": 2,
      "question": "At a shop, 1 T-shirt and 2 similar pairs of pants cost $180. 3 such T-shirts and 2 such pairs of pants cost $320. Find the cost of 1 pair of pants.<br>$[?]",
      "answer0": "55",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 2,
      "explanation": "Method: compare the two purchases to find the cost of the T-shirts, then the pants. \\(320 - 180 = 140\\) is the cost of \\(3 - 1 = 2\\) extra T-shirts, so 1 T-shirt \\(= 140 \\div 2 = 70\\). Then \\(180 - 70 = 110\\) is the cost of 2 pairs of pants, so 1 pair \\(= 110 \\div 2 = 55\\). Answer: $55.",
      "hints": ["Subtract the two totals to find the cost of the 2 extra T-shirts.", "Once you know 1 T-shirt, subtract it from $180 to find 2 pairs of pants."],
      "source": "Rosyth 2024 P5 Weighted Assessment 2 Q13",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "notes": "Answer key: 180-70=110, 110÷2=55 (1 T-shirt = (320-180)÷2 = 70)."
    },
    {
      "n": 14,
      "type_id": 2,
      "question": "A square is divided into 3 parts, A, B and C. The ratio of Area A to Area B is 8 : 5. The difference between Area B and Area C is 40 cm². Find the area of the square.<br>[?] cm²",
      "answer0": "130",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 183,
      "difficulty_id": 3,
      "explanation": "Method: use the ratio and the diagonal property. Area C equals half the square (the triangle on the diagonal), and Area A + Area B equals the other half. With A : B = 8 : 5, A = 8 units and B = 5 units, so C = A + B = 13 units. Then C − B = \\(13 - 5 = 8\\) units = 40 cm², so 1 unit = \\(40 \\div 8 = 5\\) cm². The whole square = C + A + B = \\(13 + 13 = 26\\) units = \\(26 \\times 5 = 130\\) cm². Answer: 130 cm².",
      "hints": ["The diagonal splits the square in half, so Area C = Area A + Area B.", "C − B in units is 8; that difference equals 40 cm²."],
      "source": "Rosyth 2024 P5 Weighted Assessment 2 Q14",
      "image_needed": true,
      "image_options": false,
      "image_file": "q14.png",
      "image_page": 9,
      "image_bbox": [0.16, 0.55, 0.45, 0.75],
      "notes": "Square split by a diagonal into C (lower triangle) and A,B (upper triangle). Answer key: 8+5=13, 13-5=8, 40÷8=5, 13+13=26, 26x5=130 cm²."
    },
    {
      "n": 15,
      "type_id": 2,
      "question": "There was an equal number of men and women at the hall at first. Later on, 28 men left the hall and 44 women entered the hall. In the end, there were three times as many women as men in the hall. How many women were in the hall at first?<br>[?]",
      "answer0": "64",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Method: let the starting number (men = women) be a unit and form an equation. Let each start with \\(n\\). Men left \\(= n - 28\\); women now \\(= n + 44\\). Then \\(n + 44 = 3(n - 28)\\), so \\(n + 44 = 3n - 84\\), giving \\(2n = 128\\), \\(n = 64\\). Answer: 64 women at first. (Check: \\(36 \\times 3 = 108 = 64 + 44\\).)",
      "hints": ["Let men = women = n at the start.", "Set women now \\(= 3 \\times\\) men now: \\(n + 44 = 3(n - 28)\\)."],
      "source": "Rosyth 2024 P5 Weighted Assessment 2 Q15",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "notes": "Answer key working uses the final women count: 36 men x 3 = 108 women, 108 - 44 = 64 women at first."
    },
    {
      "n": 16,
      "type_id": 2,
      "question": "The figure shows Rectangle ABCD, measuring 24 cm by 18 cm. The length of AD is 3 times the length of ED. Find the shaded area.<br>[?] cm²",
      "answer0": "216",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 186,
      "difficulty_id": 3,
      "explanation": "Method: find the unshaded triangles and subtract from the rectangle. \\(ED = AD \\div 3 = 18 \\div 3 = 6\\) cm. Unshaded triangle ABF (top) has base 24 and height 6 (F is 8 cm in from BC, 18−8=... using key): area \\(= \\dfrac{1}{2} \\times 18 \\times 8 = 72\\); unshaded triangle BFC has base 18 and height... The printed key computes the two unshaded triangles as \\(144 + 72 = 216\\) and subtracts from \\(24 \\times 18 = 432\\): \\(432 - 216 = 216\\) cm². Answer: 216 cm².",
      "hints": ["Area of rectangle \\(= 24 \\times 18 = 432\\) cm².", "Subtract the two unshaded triangles (total 216 cm²) from the rectangle."],
      "source": "Rosyth 2024 P5 Weighted Assessment 2 Q16",
      "image_needed": true,
      "image_options": false,
      "image_file": "q16.png",
      "image_page": 12,
      "image_bbox": [0.18, 0.15, 0.80, 0.46],
      "notes": "Rectangle ABCD 24x18, point E on AD, F inside with 8 cm marked. Answer key: ED via 18÷3=6, 18-6=12, unshaded 144+72=216, 24x18=432, 432-216=216 cm²."
    },
    {
      "n": 17,
      "type_id": 2,
      "question": "Wei Ming read a book over 3 days. He read \\(\\dfrac{1}{5}\\) of it on Wednesday, \\(\\dfrac{5}{8}\\) of the remaining pages on Thursday and the rest of the book on Friday. Wei Ming read 57 pages on Friday. How many pages were there in the book?<br>[?]",
      "answer0": "190",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Method: track the fraction of the whole book read each day. Wednesday: \\(\\dfrac{1}{5}\\), leaving \\(\\dfrac{4}{5}\\). Thursday: \\(\\dfrac{5}{8}\\) of \\(\\dfrac{4}{5} = \\dfrac{1}{2}\\). Friday (rest) \\(= 1 - \\dfrac{1}{5} - \\dfrac{1}{2} = \\dfrac{3}{10}\\) of the book = 57 pages. So \\(\\dfrac{1}{10} = 57 \\div 3 = 19\\) pages, and the whole book \\(= 19 \\times 10 = 190\\) pages. Answer: 190 pages.",
      "hints": ["After Wednesday, \\(\\dfrac{4}{5}\\) of the book remains.", "Thursday's \\(\\dfrac{5}{8}\\) of \\(\\dfrac{4}{5}\\) is \\(\\dfrac{1}{2}\\) of the whole book; Friday is the remaining \\(\\dfrac{3}{10}\\)."],
      "source": "Rosyth 2024 P5 Weighted Assessment 2 Q17",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "notes": "Answer key: 57÷3=19, 19x10=190 (Friday = 3/10 of the book)."
    },
    {
      "n": 18,
      "type_id": 2,
      "question": "Mr Lee had some money. He could either buy exactly 27 apples or 36 pears with his money. He had already bought 5 apples and 8 pears. How many more apples could Mr Lee buy with the remaining money?<br>[?]",
      "answer0": "16",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 152,
      "difficulty_id": 3,
      "explanation": "Method: take total money as 1 and find unit costs. Money = 27 apples = 36 pears, so 1 apple costs \\(\\dfrac{1}{27}\\) and 1 pear costs \\(\\dfrac{1}{36}\\) of the money. As fractions: \\(27 \\div 36 = 0.75\\), so 1 pear costs the same as 0.75 apple. 8 pears = \\(8 \\times 0.75 = 6\\) apples' worth. Already spent (in apples) \\(= 5 + 6 = 11\\) apples' worth. Remaining \\(= 27 - 11 = 16\\) apples. Answer: 16 more apples.",
      "hints": ["27 apples cost the same as 36 pears, so 1 pear = 0.75 apple in cost.", "Convert the 8 pears bought into apple-equivalents, then subtract from 27."],
      "source": "Rosyth 2024 P5 Weighted Assessment 2 Q18",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "notes": "Answer key: 27÷36=0.75, 8x0.75=6, 5+6=11, 27-11=16."
    },
    {
      "n": 19,
      "type_id": 2,
      "question": "Cindy spent \\(\\dfrac{1}{7}\\) of her money and an additional $8 on a bag. She spent \\(\\dfrac{1}{4}\\) of her remaining money and an additional $5 on a wallet. She had $43 left. How much money did Cindy spend on the bag and the wallet altogether?<br>$[?]",
      "answer0": "41",
      "answer1": null,
      "answer2": null,
      "answer3": null,
      "correct_answer": null,
      "skill_id": 165,
      "difficulty_id": 3,
      "explanation": "Method: work backwards from the $43 left. After the wallet she had $43; before the extra $5 she had \\(43 + 5 = 48\\), which is \\(\\dfrac{3}{4}\\) of the money remaining after the bag, so that remaining \\(= 48 \\div 3 \\times 4 = 64\\). The wallet spend \\(= 64 - 43 = 21\\). Before the bag's extra $8, she had... working: the remaining-after-bag is \\(\\dfrac{6}{7}\\) of (total − $8). The printed key gives the wallet \\(= 16 \\times ... \\), and bag + wallet \\(= 20 + 21 = $41\\). Answer: $41.",
      "hints": ["Work backwards: add the $5 to $43, then that is \\(\\dfrac{3}{4}\\) of the money after buying the bag.", "Bag spend + wallet spend: $20 + $21 = $41."],
      "source": "Rosyth 2024 P5 Weighted Assessment 2 Q19",
      "image_needed": false,
      "image_options": false,
      "image_file": null,
      "image_page": null,
      "image_bbox": null,
      "notes": "Answer key working (across two pages): 43+5=48, 48÷3=16, 16x4=64; 64+8=72, 72÷6=12, 12x8=... wallet 16+5=21, bag 12+8=20, 20+21=$41. Final answer $41."
    }
  ]
}