hnature0704 wrote:Thank you
The number of stamps that Kaye and Alberto had were in the ratio 5:3, respectively. After Kaye gave Alberto 10 of her stamps, the ratio of thenumber Kaye had to the number Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto?
1) 20
2) 30
3) 40
4) 60
5) 90
Others likely will show you the algebraic way of solving. For anyone who struggles with the algebra, this problem also can be solved quite easily -- even efficiently -- by using the following technique:
Guess and Check
Here's the situation in the problem:
Original ratio: 5/3
Exchange: Kaye loses 10, Albert gets 10
New ratio: 7/5
Let's guess and check! The goal is to determine the one set of values that will satisfy all the conditions in the problem.
Since the answer choices are all multiples of 10, we should try multiples of 10 until we find the combination that works:
Original values: Kaye has 50, Albert has 30
After the exchange: Kaye has 40, Albert has 40
Is the new ratio 7:5? 40/40 = 1/1. Doesn't work.
Let's double everything:
Original values: Kaye has 100, Albert has 60
After the exchange: Kaye has 90, Albert has 70
Is the new ratio 7:5? 90/70 = 9/7. Doesn't work.
Let's triple everything:
Original values: Kaye has 150, Albert has 90
After the exchange: Kaye has 140, Albert has 100
Is the new ratio 7:5? 140/100 = 70/50 = 7/5. Success!
Since after the exchange Kaye has 140-100 = 40 more stamps than Albert, the correct answer is
C.
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