Mark and Gem has some money each. If Gem gives Mark $15, he will have 7 times as much money as her. If Mark gives Gem $10, he will have the same amount of money as her. How much money does each person have respectively?
- Mark?
- Gem?
| |
Case 1 |
Case 2 |
| |
Mark |
Gem |
Mark |
Gem |
| Before |
7 u - 15 |
1 u + 15 |
4 u + 10 |
4 u - 10 |
| Change |
+ 15 |
- 15 |
- 10 |
+ 10 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Gem gives Mark some money or Mark gives Gem some money, the total amount of money remains the same.
Total amount that Mark and Gem have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Mark and Gem each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Mark has at first in Case 1 and Case 2 is the same.
7 u - 15 = 4 u + 10
7 u - 4 u = 10 + 15
1 u = 25
Amount that Mark has
= 4 u + 10
= 4 x 25 + 10
= 100 + 10
= $110
(b)
Amount that Gem has
= 1 u + 15
= 25 + 15
= $40
Answer(s): (a) $110; (b) $40
