Question

If Abby gives $10 to Ben, then they will have the same amount of money. If Ben gives $20 to Abby, then she'll have four times as much as he has. How much money does each of them have now?

Answer 1

Abby has $60 and Ben has $40.

Explanation:

Let a = Abby's money and b = Ben's money.

We have two conditions:

(1) a - 10 = b + 10

(2) a + 20 = 4(b - 20)

Add 10 to each side of (1) (3) a = b + 20

Distribute the 4 In (2): a + 20 = 4b - 80

Subtract 20 from each side: (4) a = 4b - 100

Subtract (3) from (4): 0 = 3b - 120

Add 120 to each side: 120 = 3b

Divide each side by 3: (5) b = 40

Substitute (5) into (1): a - 10 = 40 + 10

a - 10 = 50

Add 10 to each side: a = 60

Abby has $60 and Ben has $40.

Check:

(1) 60 - 10 = 40 + 10 (2) 60 + 20 = 4(40- 20)

50 = 50 80 = 4 × 20

80 = 80