Jack and Barbara has some money each. If Barbara gives Jack $15, he will have 7 times as much money as her. If Jack gives Barbara $13, he will have the same amount of money as her. How much money does each person have respectively?
- Jack?
- Barbara?
| |
Case 1 |
Case 2 |
| |
Jack |
Barbara |
Jack |
Barbara |
| Before |
7 u - 15 |
1 u + 15 |
4 u + 13 |
4 u - 13 |
| Change |
+ 15 |
- 15 |
- 13 |
+ 13 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Barbara gives Jack some money or Jack gives Barbara some money, the total amount of money remains the same.
Total amount that Jack and Barbara have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Jack and Barbara each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Jack has at first in Case 1 and Case 2 is the same.
7 u - 15 = 4 u + 13
7 u - 4 u = 13 + 15
1 u = 28
Amount that Jack has
= 4 u + 13
= 4 x 28 + 13
= 112 + 13
= $125
(b)
Amount that Barbara has
= 1 u + 15
= 28 + 15
= $43
Answer(s): (a) $125; (b) $43
