MATH SOLVE

3 months ago

Q:
# 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?

Accepted Solution

A:

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