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

Answer:

Abby has $60 and Ben has $40.

Step-by-step 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