Ratios Problem

neoshichhadva 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

[spoiler]Answer: C[/spoiler]

Can someone please explain how to solve?

Let the Initial number of stamps of Kaye and Alberto be 5a and 3a , ratio of stamps with Kaye & Alberto is 5a /3a


Now , Kaye gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7:5


So , 5a - 10 /3a + 10 = 7/5

25a - 50 = 21a + 70

4a = 120

So , a = 30


So initially Kaye gave Alberto had , 150 and 90 stamps....


Later , Kaye gave Alberto 10 of her stamps

So stamps with Kaye and Alberto after giving 10 stamps is :


Kaye : 140

Alberto : 100



So difference between them is 140 -100 = 40 stamps...


Option C.

5x and 3x initially.
5x-10 / 3x+10 = 7/5
25x-50 = 21x + 70
x=30
thus final: 140 and 100
140-100=40
IMO C

Kalye/Alberto = 5X/3X

After, Kayle gives Alberto 10 of her stamps,

ratio becomes - 5X-10/(3X+10) = 7/5 (New ratio given)

Solve for X; we get X=30.

Therefore; Stamps Kayle has = 5X-10 = 140
Alberto = 3X+10 = 100

Difference = 40