1) Express the old ratio as a fraction. transition from "ratio of stamps" to real number of stamps, so that you can make the change (+10/-10).

ratio is 5:3, so real numbers are 5x:3x, or 5x/3x expressed as a fraction.

2) Make the change in numerator and denominator:
Kayle gave 10 stamps, so her new quantitiy is 5x-10
Alberto got 10 stamps, so his new quantity is 3x+10

fraction is now 5x-10 / 3x+10

3) the new ratio is 7:5, so the fraction must equal the new ratio: 5x-10/3x+10 = 7/5.
Solve for x:
5(5x-10) = 7(3x+10)
25x-50 = 21x+70
4x = 120
x=30.

4) Don't choose B! what is x? it is the multiplier, needed in the transition from ratio to real number. Originally, Kayle and Alberto had 5x and 3x stamps, or 5*30=150 and 3*30=90 stamps respectively. After the change, they have 140 (10 stamps less) and 100 (10 stamps more) respectively, so as a result of this gift, Kayle has 40 more stamps. Answer is C.

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

For anyone who struggles with setting up equations, 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

Now 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.

Let the no of stamp Kayle initially has =K
Let the ...Alberto has =A

Then K/A =5/3

or 3K-5A =0 (1)

After Kayle 10 of her stamps,she has = K-10 stamps
Alberto,after receiving those stamps,has = A+10 stamps

(K-10)/(A+10) = 7/5

5K-50 = 7A+70
5K-7A =120 (2)

From 1 and 2

A =90 and K =150 [ i'm not showing that.If you don'e get it,just pm me ]

NOW the QUESTION IS " WHAT IS (K-10)-(A+10)=?"

(140)-(100)=40

Therefore C