{
    "8357": {
        "body": "Ben is 1 unit. Amy is Ben + 5 cm. Chris is Ben + 10 cm (Ben is 10 cm shorter than Chris). The three heights total 465 cm.<br><br>[[model:questions\/solutions\/q8357.png]]<br><br>• 3 units + 5 + 10 → 465 cm<br>• 3 units → 465 − 15 = 450 cm<br>• 1 unit (Ben) → 450 ÷ 3 = 150 cm<br>• Chris → 150 + 10 = 160 cm<br><br>Chris is 160 cm tall.<br>Check: Ben 150 + Amy 155 + Chris 160 = 465 cm. ✓",
        "hints": [
            "Draw the bar model first. Ben is 1 unit; Amy is Ben + 5 cm; Chris is Ben + 10 cm. The three heights total 465 cm.",
            "3 units + 5 + 10 → 465 cm",
            "Take away the two extra parts (5 and 10) so all three bars are equal — the total becomes 465 − 15 = 450 cm (3 equal units):<br>[[model:questions\/solutions\/q8357_h.png]]",
            "1 unit (Ben) → 450 ÷ 3 = 150 cm",
            "Chris → 150 + 10 = 160 cm"
        ],
        "has_h": true
    },
    "8360": {
        "body": "The 2nd piece is 1 unit. The 1st piece is 4 units (4 times the 2nd). The 3rd piece is 1 unit + 120 cm. The whole wire is 840 cm.<br><br>[[model:questions\/solutions\/q8360.png]]<br><br>• 1 + 4 + 1 = 6 units, plus 120 → 840 cm<br>• 6 units → 840 − 120 = 720 cm<br>• 1 unit (2nd) → 720 ÷ 6 = 120 cm<br>• Longest = 1st = 4 units → 4 × 120 = 480 cm<br><br>The longest piece is 480 cm.<br>Check: 2nd 120 + 1st 480 + 3rd 240 = 840 cm. ✓",
        "hints": [
            "Draw the bar model first. 2nd piece = 1 unit, 1st piece = 4 units, 3rd piece = 1 unit + 120 cm. The wire is 840 cm.",
            "1 + 4 + 1 = 6 units, plus 120 → 840 cm",
            "Remove the extra 120 cm so the bars are whole units — the total becomes 840 − 120 = 720 cm (6 equal units):<br>[[model:questions\/solutions\/q8360_h.png]]",
            "1 unit (2nd) → 720 ÷ 6 = 120 cm",
            "Longest = 1st = 4 units → 4 × 120 = 480 cm"
        ],
        "has_h": true
    },
    "8361": {
        "body": "B is 1 unit. A is 5 units (5 times B). C is A − 400 = 5 units − 400. The three containers total 2900 ml.<br><br>[[model:questions\/solutions\/q8361.png]]<br><br>• 1 + 5 + 5 = 11 units, − 400 → 2900 ml<br>• 11 units → 2900 + 400 = 3300 ml<br>• 1 unit (B) → 3300 ÷ 11 = 300 ml<br><br>Container B has 300 ml.<br>Check: B 300 + A 1500 + C 1100 = 2900 ml. ✓",
        "hints": [
            "Draw the bar model first. B = 1 unit, A = 5 units, C = 5 units − 400. The three containers total 2900 ml.",
            "1 + 5 + 5 = 11 units, − 400 → 2900 ml",
            "Add the missing 400 ml back onto C so every bar is whole units — the total becomes 2900 + 400 = 3300 ml (11 equal units):<br>[[model:questions\/solutions\/q8361_h.png]]",
            "1 unit (B) → 3300 ÷ 11 = 300 ml"
        ],
        "has_h": true
    },
    "8366": {
        "body": "Both rows contain the same 450 g bag, so the bag cancels out. The extra mass in the first row comes only from the 7 − 4 = 3 extra boxes.<br><br>[[model:questions\/solutions\/q8366.png]]<br><br>• Difference → 3950 − 2450 = 1500 g<br>• 3 boxes → 1500 g<br>• 1 box → 1500 ÷ 3 = 500 g<br><br>One box has a mass of 500 g.<br>Check: 7(500) + 450 = 3950 g; 4(500) + 450 = 2450 g. ✓",
        "hints": [
            "Draw both rows as bars. Each row has the same 450 g bag plus some equal boxes. The bag is the same in both, so it cancels.",
            "Difference → 3950 − 2450 = 1500 g",
            "Line the two rows up: the bag cancels and only the 7 − 4 = 3 extra boxes are left over — those 3 boxes weigh the 1500 g difference:<br>[[model:questions\/solutions\/q8366_h.png]]",
            "1 box → 1500 ÷ 3 = 500 g"
        ],
        "has_h": true
    },
    "8370": {
        "body": "B is 1 unit. A is 2 units (twice B). C is B + 80 = 1 unit + 80. D is the same as A = 2 units. The four bags total 1460 g.<br><br>[[model:questions\/solutions\/q8370.png]]<br><br>• 1 + 2 + 1 + 2 = 6 units, plus 80 → 1460 g<br>• 6 units → 1460 − 80 = 1380 g<br>• 1 unit (B) → 1380 ÷ 6 = 230 g<br><br>Bag B has a mass of 230 g.<br>Check: B 230 + A 460 + C 310 + D 460 = 1460 g. ✓",
        "hints": [
            "Draw the bar model first. B = 1 unit, A = 2 units, C = 1 unit + 80, D = 2 units (same as A). Total 1460 g.",
            "1 + 2 + 1 + 2 = 6 units, plus 80 → 1460 g",
            "Remove the extra 80 g from C so all bars are whole units — the total becomes 1460 − 80 = 1380 g (6 equal units):<br>[[model:questions\/solutions\/q8370_h.png]]",
            "1 unit (B) → 1380 ÷ 6 = 230 g"
        ],
        "has_h": true
    },
    "8379": {
        "body": "Q is 1 unit. P is 2 units (twice Q). R is Q + 80 = 1 unit + 80. S is a fixed 200 g. The four boxes total 960 g.<br><br>[[model:questions\/solutions\/q8379.png]]<br><br>• 1 + 2 + 1 = 4 units, plus 80 + 200 → 960 g<br>• 4 units → 960 − 280 = 680 g<br>• 1 unit (Q) → 680 ÷ 4 = 170 g<br>• P = 2 units → 2 × 170 = 340 g<br><br>Box P has a mass of 340 g.<br>Check: Q 170 + P 340 + R 250 + S 200 = 960 g. ✓",
        "hints": [
            "Draw the bar model first. Q = 1 unit, P = 2 units, R = 1 unit + 80, S = 200 g (fixed). Total 960 g.",
            "1 + 2 + 1 = 4 units, plus 80 + 200 → 960 g",
            "Take out the fixed parts (R’s extra 80 g and S’s 200 g) so only whole units remain — the total becomes 960 − 280 = 680 g (4 equal units):<br>[[model:questions\/solutions\/q8379_h.png]]",
            "1 unit (Q) → 680 ÷ 4 = 170 g",
            "P = 2 units → 2 × 170 = 340 g"
        ],
        "has_h": true
    },
    "8214": {
        "body": "Oranges = 1 unit. Apples = 2 units (twice the oranges). Bananas = apples + 50 = 2 units + 50. The basket holds 400 fruits.<br><br>[[model:questions\/solutions\/q8214.png]]<br><br>• 1 + 2 + 2 = 5 units, plus 50 → 400<br>• 5 units → 400 − 50 = 350<br>• 1 unit (oranges) → 350 ÷ 5 = 70<br>• Apples = 2 units → 2 × 70 = 140<br><br>There are 140 apples.<br>Check: oranges 70 + apples 140 + bananas 190 = 400. ✓",
        "hints": [
            "Draw the bar model first. Oranges = 1 unit, apples = 2 units, bananas = 2 units + 50. Total 400 fruits.",
            "1 + 2 + 2 = 5 units, plus 50 → 400",
            "Remove the extra 50 bananas so all bars are whole units — the total becomes 400 − 50 = 350 (5 equal units):<br>[[model:questions\/solutions\/q8214_h.png]]",
            "1 unit (oranges) → 350 ÷ 5 = 70",
            "Apples = 2 units → 2 × 70 = 140"
        ],
        "has_h": true
    },
    "8222": {
        "body": "Gummies = 1 unit. Chocolates = 3 units (3 times the gummies). Lollipops = chocolates + 70 = 3 units + 70. There are 490 candies in all.<br><br>[[model:questions\/solutions\/q8222.png]]<br><br>• 1 + 3 + 3 = 7 units, plus 70 → 490<br>• 7 units → 490 − 70 = 420<br>• 1 unit (gummies) → 420 ÷ 7 = 60<br>• Chocolates = 3 units → 3 × 60 = 180<br><br>There are 180 chocolates.<br>Check: gummies 60 + chocolates 180 + lollipops 250 = 490. ✓",
        "hints": [
            "Draw the bar model first. Gummies = 1 unit, chocolates = 3 units, lollipops = 3 units + 70. Total 490 candies.",
            "1 + 3 + 3 = 7 units, plus 70 → 490",
            "Remove the extra 70 lollipops so all bars are whole units — the total becomes 490 − 70 = 420 (7 equal units):<br>[[model:questions\/solutions\/q8222_h.png]]",
            "1 unit (gummies) → 420 ÷ 7 = 60",
            "Chocolates = 3 units → 3 × 60 = 180"
        ],
        "has_h": true
    }
}