Carcass wrote:
Jennifer has 60 dollars more than Brian. If she were to give Brian 1/5 of her money, Brian would have 25% less than the amount that Jennifer would then have. How much money does Jennifer have?
Here's one approach:
Let J = Jennifer's $
Let B = Brian's $
Jennifer has 60 dollars more than Brian.So,
J = B + 60If Jennifer were to give Brian 1/5 of her money, Brian would have 25% less than the amount that Jennifer would then have. If Jennifer were to give Brian 1/5 of her money, then Jennifer has
(4/5)J dollars, and Brian has
B + (1/5)J dollars
If Brian has 25% less than the amount that Jennifer has, then Brian's amount = 3/4 Jennifer's amount.
So, we can write: (3/4)
(4/5)J =
B + (1/5)J Simplify, to get (3/5)J = B + (1/5)J
Multiply both sides by 5 to get: 3J = 5B + J
Rearrange:
2J = 5BWe now have the system:
J = B + 602J = 5BWhen we solve it, we get J = 100 (as well as B = 40)
Answer: 100
Cheers,
Brent