Sam and Barbara has some money each. If Barbara gives Sam $14, he will have 5 times as much money as her. If Sam gives Barbara $15, he will have the same amount of money as her. How much money does each person have respectively?
- Sam?
- Barbara?
| |
Case 1 |
Case 2 |
| |
Sam |
Barbara |
Sam |
Barbara |
| Before |
5 u - 14 |
1 u + 14 |
3 u + 15 |
3 u - 15 |
| Change |
+ 14 |
- 14 |
- 15 |
+ 15 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Barbara gives Sam some money or Sam gives Barbara some money, the total amount of money remains the same.
Total amount that Sam and Barbara have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Sam and Barbara each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Sam has at first in Case 1 and Case 2 is the same.
5 u - 14 = 3 u + 15
5 u - 3 u = 15 + 14
1 u = 29
Amount that Sam has
= 3 u + 15
= 3 x 29 + 15
= 87 + 15
= $102
(b)
Amount that Barbara has
= 1 u + 14
= 29 + 14
= $43
Answer(s): (a) $102; (b) $43
