Pierre and Gem has some money each. If Gem gives Pierre $11, he will have 5 times as much money as her. If Pierre gives Gem $18, he will have the same amount of money as her. How much money does each person have respectively?
- Pierre?
- Gem?
| |
Case 1 |
Case 2 |
| |
Pierre |
Gem |
Pierre |
Gem |
| Before |
5 u - 11 |
1 u + 11 |
3 u + 18 |
3 u - 18 |
| Change |
+ 11 |
- 11 |
- 18 |
+ 18 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Gem gives Pierre some money or Pierre gives Gem some money, the total amount of money remains the same.
Total amount that Pierre and Gem have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Pierre and Gem each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Pierre has at first in Case 1 and Case 2 is the same.
5 u - 11 = 3 u + 18
5 u - 3 u = 18 + 11
1 u = 29
Amount that Pierre has
= 3 u + 18
= 3 x 29 + 18
= 87 + 18
= $105
(b)
Amount that Gem has
= 1 u + 11
= 29 + 11
= $40
Answer(s): (a) $105; (b) $40
