Question

Ally collects stickers as a hobby. She gives her sister 1/5 of her stickers. She then gives her cousin 1/5 of the remainder. Ally says that she has of the stickers in the end because1-1/5-1/5= 3/5

Explain why Ally's reasoning is incorrect. What should the correct answer be?

Answer 1

Ally's reasoning is incorrect because she double-counts the stickers she gives away.

Ally only has 12/25 of her original collection of stickers left, not 3/5.

.When she gives away 1/5 of her stickers to her sister, she is left with 4/5 of her original collection. However, when she then gives away 1/5 of the remaining stickers to her cousin, she is giving away 1/5 of 4/5 of her original collection, not 1/5 of the entire collection.

Therefore, the correct answer should be calculated as follows:

Start with the original number of stickers: x

Give away 1/5 to the sister: x - 1/5x = 4/5x

Give away 1/5 of the remaining stickers to the cousin: 4/5x - 1/5(4/5x) = 4/5x - 4/25x = 12/25x

Calculate the proportion of stickers Ally has left: 12/25*x / x

= 12/25

Therefore, Ally only has 12/25 of her original collection of stickers left, not 3/5.