The number of baseball cards that John and Bill...

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

The number of baseball cards that John and Bill...

by swerve » Thu Feb 08, 2018 6:10 am

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

The OA is B.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

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Source: Beat The GMAT — Problem Solving | Thu Feb 08, 2018 6:10 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Thu Feb 08, 2018 7:17 am

swerve 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

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

Brent Hanneson - Creator of GMATPrepNow.com

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Jul 01, 2019 4:26 pm

swerve 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

We can let the original number of baseball cards John and Bill had be 7x and 3x, respectively. So we can create the equation:

(7x - 15)/(3x + 15) = 3/2

2(7x - 15) = 3(3x + 15)

14x - 30 = 9x + 45

5x = 75

x = 15

Therefore, John and Bill originally had 105 and 45 cards, respectively. After John gave Bill 15 cards, John now had 90 cards and Bill had 60 cards. So John had 30 more cards than Bill.

Answer: B

Scott Woodbury-Stewart
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