Tom and Barbara has some money each. If Barbara gives Tom $20, he will have 7 times as much money as her. If Tom gives Barbara $12, he will have the same amount of money as her. How much money does each person have respectively?
- Tom?
- Barbara?
|
Case 1 |
Case 2 |
|
Tom |
Barbara |
Tom |
Barbara |
Before |
7 u - 20 |
1 u + 20 |
4 u + 12 |
4 u - 12 |
Change |
+ 20 |
- 20 |
- 12 |
+ 12 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Barbara gives Tom some money or Tom gives Barbara some money, the total amount of money remains the same.
Total amount that Tom and Barbara have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Tom and Barbara each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Tom has at first in Case 1 and Case 2 is the same.
7 u - 20 = 4 u + 12
7 u - 4 u = 12 + 20
1 u = 32
Amount that Tom has
= 4 u + 12
= 4 x 32 + 12
= 128 + 12
= $140
(b)
Amount that Barbara has
= 1 u + 20
= 32 + 20
= $52
Answer(s): (a) $140; (b) $52