Jenson and Gem has some money each. If Gem gives Jenson $18, he will have 5 times as much money as her. If Jenson gives Gem $17, he will have the same amount of money as her. How much money does each person have respectively?
- Jenson?
- Gem?
| |
Case 1 |
Case 2 |
| |
Jenson |
Gem |
Jenson |
Gem |
| Before |
5 u - 18 |
1 u + 18 |
3 u + 17 |
3 u - 17 |
| Change |
+ 18 |
- 18 |
- 17 |
+ 17 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Gem gives Jenson some money or Jenson gives Gem some money, the total amount of money remains the same.
Total amount that Jenson and Gem have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Jenson and Gem each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Jenson has at first in Case 1 and Case 2 is the same.
5 u - 18 = 3 u + 17
5 u - 3 u = 17 + 18
1 u = 35
Amount that Jenson has
= 3 u + 17
= 3 x 35 + 17
= 105 + 17
= $122
(b)
Amount that Gem has
= 1 u + 18
= 35 + 18
= $53
Answer(s): (a) $122; (b) $53
