Schrute Beets 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
Thanks!
If you're not so good with ratios, this would be great problem to solve by
guessing and checking.
When you're guessing and checking,
let the answer choices guide you. Since the answer choices in this problem are all multiples of 10, let's try some multiples of 10 that satisfy K/A = 5/3:
K=50, A=30
K=100, A=60
K=150, A=90
If K gives 10 stamps to Albert, the resulting ratio is (K-10)/(A+10) = 7/5, so K-10 must be a multiple of 7.
Only K=150 works, because 150-10=140.
So let's try K=150, A=90.
K-10 = 150-10 = 140.
A+10 = 90+10 = 100.
140/100 = 14/10 = 7/5. Success!
K-A = 140-100 = 40.
The correct answer is C.
If you let the answer choices guide you, guessing and checking can be a safe and efficient way to solve many tough problems. (And no risk of making an algebraic error!)
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