Viper83 wrote: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 the number Kaye had to the number Alberto had was 7:5. As a result of this gift, Kaye had how many more stamps than Alberto?
A) 20
B) 30
C) 40
D) 60
E) 90
C
I've amended the question to reflect its actual wording.
Here is a way to solve the problem very quickly without having to set up any algebraic equations.
Since the original ratio is 5:3, and 5+3 = 8, Kaye starts with 5/8 of the stamps.
Since the final ratio is 7:5, and 7+5 = 12, Kaye finishes with 7/12 of the stamps.
Since all the answer choices are multiples of 10, and Kaye starts with 5/8 of the stamps and finishes with 7/12 of the stamps, the total number of stamps must be a multiple of 8, 10 and 12.
The LCM (lowest common multiple) of 8, 10 and 12 = 120.
Let stamps = 120.
Start: Kaye has (5/8)*120 = 75, Albert has 120-75 = 45.
Finish: Kaye has (7/12)*120 = 70, Albert has 120-70 = 50.
Number of stamps Kaye gives Alberto = 75-70 = 5.
Since Kaye needs to give Alberto twice as many stamps, the total number of stamps -- in fact, ALL the values above -- must double.
Finish doubled: Kaye has 2*70 = 140 stamps, Albert has 2*50 = 100 stamps.
Difference between Kaye and Alberto = 140-100 = 40.
The correct answer is
C.
Here are all the values when doubled:
Let stamps = 240.
Start: Kaye has (5/8)*240 = 150, Albert has 240-150 = 90.
Finish: Kaye has (7/12)*240 = 140, Albert has 240-140 = 100.
Number of stamps Kaye gives Alberto = 150-140 = 10.
Success!
Difference between Kaye and Alberto at the finish = 140-100 = 40.
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