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The number of baseball cards that John and Bill had was in the ratio o
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09 Apr 2021, 05:15
09 Apr 2021, 05:15
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68% (02:14) correct
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The number of baseball cards that John and Bill had was in the ratio of 7:3. After John gave Bill 15 of his baseball cards, the ratio of the number of baseball cards that John had to the number that Bill had was 3:2. After the gift, John had how many more baseball cards than Bill?
A. 15
B. 30
C. 45
D. 60
E. 90
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 15
B. 30
C. 45
D. 60
E. 90
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: The number of baseball cards that John and Bill had was in the ratio o
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09 Apr 2021, 09:42
09 Apr 2021, 09:42
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Carcass wrote:
The number of baseball cards that John and Bill had was in the ratio of 7:3. After John gave Bill 15 of his baseball cards, the ratio of the number of baseball cards that John had to the number that Bill had was 3:2. After the gift, John had how many more baseball cards than Bill?
A. 15
B. 30
C. 45
D. 60
E. 90
A. 15
B. 30
C. 45
D. 60
E. 90
\(\frac{J}{B} = \frac{7}{3}\)
\(\frac{J-15}{B+15} = \frac{3}{2}\)
Equating \(J\) form both the equations;
\(\frac{7B}{3} = \frac{3(B + 15)}{2} + 15\)
\(14B = 9B + 225\)
\(B = 45\)
\(J = \frac{7(45)}{3} = 105\)
John had how many more baseball cards than Bill \(= (J - 15) - (B + 15) = J - B - 30 = 105 - 45 - 30 = 30\)
Hence, option B
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Re: The number of baseball cards that John and Bill had was in the ratio o
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09 Apr 2021, 05:47
09 Apr 2021, 05:47
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Carcass wrote:
The number of baseball cards that John and Bill had was in the ratio of 7:3. After John gave Bill 15 of his baseball cards, the ratio of the number of baseball cards that John had to the number that Bill had was 3:2. After the gift, John had how many more baseball cards than Bill?
A. 15
B. 30
C. 45
D. 60
E. 90
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 15
B. 30
C. 45
D. 60
E. 90
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
One option is to solve the question using 2 variables
Let J = # of cards that John INITIALLY had
Let B = # of cards that Bill INITIALLY had
The number of baseball cards that John and Bill had was in the ratio of 7:3
So, we can write: J/B = 7/3
Cross multiply to get: 3J = 7B
Rearrange to get: 3J - 7B = 0
After John gave Bill 15 of his baseball cards, the ratio of the number of baseball cards that John had to the number that Bill had was 3:2.
So, John now has J - 15 cards and Bill now has B + 15 cards
We can write: J/B = (J - 15)/(B + 15) = 3/2
Cross multiply to get: (2)(J - 15) = (3)(B + 15)
Expand: 2J - 30 = 3B + 45
Rearrange to get: 2J - 3B = 75
So, we now have the following system:
3J - 7B = 0
2J - 3B = 45
Solve to get: J = 105 and B = 45
NOTE: these are the number of cards they INITIALLY had
After the gift, John had how many more baseball cards than Bill?
AFTER THE GIFT, John had 90 cards and Bill had 60 cards
So, John had 30 more cards than John.
Answer: B
Cheers,
Brent
