The number of stamps that Kaye and Alberto had were in the ration of 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto?
A. 20
B. 30
C. 40
D. 60
E. 90
The OA is C.
I get the solution in the following way,
K = Kaye
A = Alberto
K / A = 5 / 3 - - - - - - - - - (1)
(K - 10) / (A + 10) = 7 / 5 - - - - - (2)
Substitute values from 1 in 2
A = 90
K = 150
As a result of the gift, Alberto has A + 10 = 100 and Kaye has K - 10 = 140 and the difference between them is 40. Option C.
Please, can anyone explain another way to solve this PS question? Thanks!
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The number of stamps that Kaye and Alberto had were...
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One option is to solve the question using TWO VARIABLES.BTGmoderatorLU wrote:The number of stamps that Kaye and Alberto had were in the ration of 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto?
A. 20
B. 30
C. 40
D. 60
E. 90
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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The answer choices imply that the values in the problem are all MULTIPLES OF 10.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?
20
30
40
60
900
Since K:A = 5:3, the following options are implied:
K=50, A=30
K=100, A=60
K=150, A=90
K=200, A=120.
After K gives away 10 stamps and A receives 10 stamps, the resulting values for K and A must be in a ratio of 7 to 5:
K=40, A=40
K=90, A=70
K=140, A=100.
We can stop here, since 140:100 = 14:10 = 7:5.
Thus, after the exchange, K-A = 140-100 = 40.
The correct answer is C.
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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:BTGmoderatorLU wrote:The number of stamps that Kaye and Alberto had were in the ration of 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the 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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Another method is to use ratios:
Note that the total number of stamps is the same in both the cases.
On ratio scale, 5:3 gives 8 total stamps while 7:5 gives 12 total stamps. So total stamps must be at least LCM of 8 and 12 i.e. 24.
So in first case, Kaye had 15 stamps while Alberto had 9. After the exchange, Kaye had 14 stamps while Alberto had 10. So Kaye gave 1 stamp to Alberto. But actually, Kaye gave 10 stamps to Alberto. So actual total number of stamps is 240.
So the multiplier of 7:5 is 20 (because 12*20 = 240). Kaye had (7-5)*20 = 40 more stamps than Alberto.
Regards!
Note that the total number of stamps is the same in both the cases.
On ratio scale, 5:3 gives 8 total stamps while 7:5 gives 12 total stamps. So total stamps must be at least LCM of 8 and 12 i.e. 24.
So in first case, Kaye had 15 stamps while Alberto had 9. After the exchange, Kaye had 14 stamps while Alberto had 10. So Kaye gave 1 stamp to Alberto. But actually, Kaye gave 10 stamps to Alberto. So actual total number of stamps is 240.
So the multiplier of 7:5 is 20 (because 12*20 = 240). Kaye had (7-5)*20 = 40 more stamps than Alberto.
Regards!
