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Problem Solving-Variables

tagged by: rolandprowess

This topic has 1 expert reply and 2 member replies
jd6199 Newbie | Next Rank: 10 Posts
Joined
07 Jan 2007
Posted:
5 messages

Problem Solving-Variables

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?

GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
11409 messages
Followed by:
1229 members
5254
GMAT Score:
770
Sun Dec 03, 2017 10:40 am
Quote:
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

Cheers,
Brent

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Top Member

Roland2rule Legendary Member
Joined
30 Aug 2017
Posted:
713 messages
Followed by:
4 members
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

g2000 Junior | Next Rank: 30 Posts
Joined
09 Jan 2007
Posted:
19 messages
1
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.
A = A + 10 = 90 + 10 = 100
K = K - 10 = 150 - 10 = 140

How many more?
140-100 = 40

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