How much does each have before and after earning the $2?

Question

Bessy has 7 times as much money as Bob, but when each earns $2, Bessy will have 4 times as much money as Bob. How much does each have before and after earning the $2?.

Answer 1

Let's say Bob started with x dollars

Then Bessy started with 7x dollars

 

After they each earn $2, then Bob will have (x + 2) dollars and Bessy will have 7x + 2 dollars. So, we have the following equation:

 

7x + 2 = 4(x + 2)

7x + 2 = 4x + 8

3x = 6

x = 2

 

Bob started with $2 and Bessy started with 7 * 2 = $14

Answer 2

assume Betsy has $y and Bob has $b

equation 1

y = 7b

equation 2

(y+2) = 4 (b+2)

 

in equation 2, replace y with 7b

7b + 2 = 4b + 8

3b = 6

b = $2 (Bob initially had $2 and then $4 after he acquired the $2)

y = 7b = 7 x 2 = $14 (Betsy initially had $14 and then $16 after she acquired the $2)