The ratio of Mei Ling's savings to Stan's savings was 2 : 5. Each of them then saved another $30. The new ratio of Mei Ling's savings to Stan's savings became 5 : 11. How much money did Mei Ling have at first?
Show Worked Solution
Worked Solution
Step 1: Spot the invariant — when both save the SAME amount, the DIFFERENCE between their savings stays constant.
Step 2: Original difference (Stan − Mei Ling) = 5u − 2u = 3u, where u is the original unit.
Step 3: New ratio 5 : 11 means new difference = 11p − 5p = 6p, where p is the new unit. Since the difference is unchanged, 6p = 3u, so p = ½u.
Step 4: New Mei Ling's savings = 5p = 5 × ½u = 2.5u. But this also equals 2u + $30 (her original plus the $30 she added). So 2.5u − 2u = 0.5u = $30 → u = $60.
Step 5: Mei Ling at first = 2u = 2 × $60 = $120.
Answer: $120
Correct answer: $120
Want more questions like this? Superholic Lab has 10,000+ MOE-aligned questions with full worked solutions.
Start Free Trial — 7 Days Free