Howard and Gem has some money each. If Gem gives Howard $15, he will have 5 times as much money as her. If Howard gives Gem $12, he will have the same amount of money as her. How much money does each person have respectively?
- Howard?
- Gem?
| |
Case 1 |
Case 2 |
| |
Howard |
Gem |
Howard |
Gem |
| Before |
5 u - 15 |
1 u + 15 |
3 u + 12 |
3 u - 12 |
| Change |
+ 15 |
- 15 |
- 12 |
+ 12 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Gem gives Howard some money or Howard gives Gem some money, the total amount of money remains the same.
Total amount that Howard and Gem have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Howard and Gem each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Howard has at first in Case 1 and Case 2 is the same.
5 u - 15 = 3 u + 12
5 u - 3 u = 12 + 15
1 u = 27
Amount that Howard has
= 3 u + 12
= 3 x 27 + 12
= 81 + 12
= $93
(b)
Amount that Gem has
= 1 u + 15
= 27 + 15
= $42
Answer(s): (a) $93; (b) $42
