Farina wrote:
Jennifer has $400 more than Brian has. If she were to give Brian 20% of her money, then Brian would have \(\frac{2}{3}\) of the amount of money that Jennifer would then have. How much money does Brian currently have (before exchanging money)?
Here's one approach:
Let J = Jennifer's $
Let B = Brian's $
Jennifer has $400 more than Brian.So,
J = B + 400If Jennifer were to give Brian 20% of her money, Brian would have 2/3 of the amount that Jennifer would then have. 20% of Jennifer's money = 1/5 of Jennifer's money = (1/5)J
So, if Jennifer gives Brian 1/5 of her money, then Jennifer now has
(4/5)J dollars remaining, and Brian now has
B + (1/5)J dollars
If Brian now has 2/3 of the amount that Jennifer now has, then: 2/3 of Jennifer's amount = Brian's amount
So, we can write: (2/3)
(4/5)J =
B + (1/5)J Simplify, to get (8/15)J = B + (1/5)J
Multiply both sides by 15 to get: 8J = 15B + 3J
Rearrange: 5J = 15B
Divide both sides by 5 to get:
J = 3BWe now have the system:
J = B + 400J = 3BWhen we solve it, we get B = 200 (as well as J = 600)
Answer: 200
Cheers,
Brent