Use the given first number to find the unit value, then work through the changes.
[[model:questions/solutions/q10432.png]]
Red beads : blue beads = 5 : 4. There were 150 red beads at first.
• \(5u = 150\), so \(u = 30\). Blue beads at first = \(4 \times 30 = 120\).
• After removing 20% of red beads: red remaining = 80% of 150 = 120.
• Let \(b\) blue beads be added. Blue after = \(120 + b\).
• New ratio red : blue = 120 : \((120 + b) = 2 : 3\).
• \(\frac{120}{120 + b} = \frac{2}{3}\)
• \(360 = 240 + 2b\), so \(2b = 120\), \(b = 60\).
60 blue beads were added.
Check: Red = 120, Blue = 180; ratio = 120:180 = 2:3. ✓