Glen and Jaslyn has some money each. If Jaslyn gives Glen $16, he will have 5 times as much money as her. If Glen gives Jaslyn $18, he will have the same amount of money as her. How much money does each person have respectively?
- Glen?
- Jaslyn?
| |
Case 1 |
Case 2 |
| |
Glen |
Jaslyn |
Glen |
Jaslyn |
| Before |
5 u - 16 |
1 u + 16 |
3 u + 18 |
3 u - 18 |
| Change |
+ 16 |
- 16 |
- 18 |
+ 18 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Jaslyn gives Glen some money or Glen gives Jaslyn some money, the total amount of money remains the same.
Total amount that Glen and Jaslyn have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Glen and Jaslyn each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Glen has at first in Case 1 and Case 2 is the same.
5 u - 16 = 3 u + 18
5 u - 3 u = 18 + 16
1 u = 34
Amount that Glen has
= 3 u + 18
= 3 x 34 + 18
= 102 + 18
= $120
(b)
Amount that Jaslyn has
= 1 u + 16
= 34 + 16
= $50
Answer(s): (a) $120; (b) $50
