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?
Problem Solving-Variables
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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
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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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
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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One option is to solve the question using TWO VARIABLES.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
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
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We are given that the number of stamps that Kaye and Alberto had was in the ratio 5 : 3. We can represent this as: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
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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