The number of baseball cards that John and Bill had was in the ratio of 7:3

BTGModeratorVI wrote: ↑

Sun Sep 27, 2020 7:05 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

Answer: B
Source: Veritas Prep

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