Ahmad and Benny share stickers in the ratio 2 : 5. After Ahmad is given 18 more stickers, the ratio of Ahmad's stickers to Benny's stickers becomes 4 : 5. How many stickers does Benny have?
Show Worked Solution
Worked Solution
Step 1: Let each unit of the original ratio represent k stickers.
Ahmad originally has 2k stickers.
Benny originally has 5k stickers.
Step 2: After Ahmad receives 18 more stickers, set up an equation using the new ratio 4 : 5.
(2k + 18) : 5k = 4 : 5
Step 3: Cross-multiply and solve for k.
5 × (2k + 18) = 4 × 5k
10k + 90 = 20k
90 = 10k
k = 9
Step 4: Find Benny's number of stickers (Benny's count did not change).
Benny = 5k = 5 × 9 = 45
Step 5: Verify the new ratio.
Ahmad new = 2(9) + 18 = 36
36 : 45 = 4 : 5 ✓
Answer: Benny has 45 stickers.
Correct answer: 45
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