Problem Solving-Variables

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Problem Solving-Variables

by jd6199 » Sat Jan 20, 2007 11:23 am
SOURCE: PEARSON PRACTICE TEST 1

THE NUMBER OF STAMPS THAT KAYE AND ALBERTO HAD WERE IN THE RATIO OF 5:3 RESPECTIVELY. AFTER KAYE GAVE ALBERTO 10 OF HER STAMPS THE RATIO BECAME 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

CORRECT ANSWER IS C. HOW TO CALCULATE?

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my answer

by g2000 » Sat Jan 20, 2007 9:28 pm
Let A be the number of stamps Alberto has and K be the # stamps Kaye has.

K/A = 5/3
(K-10)/(A+10) = 7/5

Solve this equation for A and K and get A=90 and K=150

That's the number before the gift.
After the gift
A = A + 10 = 90 + 10 = 100
K = K - 10 = 150 - 10 = 140

How many more?
140-100 = 40

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by BTGmoderatorRO » Sun Dec 03, 2017 9:26 am
Let the number of stamp Kaye an Alberto have be x and y respectively.
At first, x : y = 5:3
or $$\frac{x}{y}$$ = $$\frac{5}{3}$$
5y = 3x or 3x-5y = 0 ....................................equation 1
As a rsult of the gift Kaye now has (x-10) stamps and Alberto have (y+10) stamps, and the ratio is x-10 : y+10 = 7:5
or
$$\frac{x-10}{y+10}$$ $$\frac{7}{5}$$
= 5(x-10) = 7(y+10)
5x-50 = 7y+70
or 5x-7y = 120.........equation 2
Solving the two equations simultaneously, we have:
3x-5y=0......(i) * 5
5x-7y=120.......(ii) * 3
Now we have 15x -25y=0
- 15x-21y=360
--------------------------------
-4y =-360
or y= $$\frac{360}{4}$$
=90
SInce y = 90, 3x-5(90) =0
3x=450, 450/3
x=150

As a result of the gift KAye has (150-10)stamps, which is 140, and Alberto now have (90+10 =100) stamps
Therefore, the ratio of their number of stamps will be
= 140:100
=14:10
=7;5
which means we are correct.
Therefore, as a result of the gift Kaye have
(1140-100) stamps more than Alberto
=40 stamps

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by Brent@GMATPrepNow » Sun Dec 03, 2017 10:40 am
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. 6O
E. 9O
One option is to solve the question using TWO VARIABLES.
Let K = # of stamps K had after the exchange
Let A = # of stamps A had after the exchange
This means that K+10 = # of stamps K had before the exchange
This means that A-10 = # of stamps A had before the exchange

Note: Our goal is to find the value of K-A

The number of stamps that K and A (originally) had were in the ratio 5:3
So, (K+10)/(A-10) = 5/3
We want a prettier equation, so let's cross multiply to get 3(K+10) = 5(A-10)
Expand: 3K + 30 = 5A - 50
Rearrange: 3K - 5A = -80

After K gave A 10 of her stamps, the ratio of the number K had to the number A had was 7:5
So, K/A = 7/5
We want a prettier equation, so let's cross multiply to get 5K = 7A
Rearrange to get: 5K - 7A = 0

At this point we have two equations:
5K - 7A = 0
3K - 5A = -80

Our goal is to find the value of K - A.
IMPORTANT: We need not solve for the individual values of K and A. This is great, because something nice happens when we subtract the blue equation from the red equation.
We get: 2K - 2A = 80
Now divide both sides by 2 to get: K - A = 40

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Scott@TargetTestPrep » Thu Oct 03, 2019 11:08 am
jd6199 wrote:SOURCE: PEARSON PRACTICE TEST 1

THE NUMBER OF STAMPS THAT KAYE AND ALBERTO HAD WERE IN THE RATIO OF 5:3 RESPECTIVELY. AFTER KAYE GAVE ALBERTO 10 OF HER STAMPS THE RATIO BECAME 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
We are given that the number of stamps that Kaye and Alberto had was in the ratio 5 : 3. We can represent this as:

K : A = 5x : 3x

We are next given that after Kaye gave Alberto 10 of her stamps, the ratio of the number Kaye had to the number Alberto had was 7 : 5. Using this information, we can create the following equation:

(5x - 10)/(3x + 10) = 7/5

5(5x - 10) = 7(3x + 10)

25x - 50 = 21x + 70

4x = 120

x = 30

Kaye now has 5(30) - 10 = 140 stamps, and Alberto has 3(30) + 10 = 100 stamps. So Kaye has 140 - 100 = 40 more stamps than Alberto has.

Answer: C

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