Question

if abby gives $10 to ben, then they will have the same mount of money. if ben gives $20 to abby, then shell have four times as much as he has. how much money does each of them have?

Answer 1

• Abby: $60
• Ben: $40

Explanation:

You want to know how much money Abby and Ben each have if when Abby gives $10 to Ben, then they will have the same mount of money. If Ben gives $20 to Abby, then she'll have four times as much as he has.

Setup

The transfers give rise to two equations:

(A-10) = (B +10)

(A +20) = 4(B -20)

Solution

Using the first equation, we can write an expression for A:

A = B +20

This can be substituted into the second equation to give ...

(B +20) +20 = 4(B -20)

B +40 = 4B -80 . . . . simplify

120 = 3B . . . . . . . . . . add 80-B

40 = B . . . . . . . . . . . . divide by 3

A = B +20 = 60 . . . . Abby's amount

Abby has $60; Ben has $40.