Gabriel and Shannon has some money each. If Shannon gives Gabriel $16, he will have 3 times as much money as her. If Gabriel gives Shannon $20, he will have the same amount of money as her. How much money does each person have respectively?
- Gabriel?
- Shannon?
| |
Case 1 |
Case 2 |
| |
Gabriel |
Shannon |
Gabriel |
Shannon |
| Before |
3 u - 16 |
1 u + 16 |
2 u + 20 |
2 u - 20 |
| Change |
+ 16 |
- 16 |
- 20 |
+ 20 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Shannon gives Gabriel some money or Gabriel gives Shannon some money, the total amount of money remains the same.
Total amount that Gabriel and Shannon have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Gabriel and Shannon each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Gabriel has at first in Case 1 and Case 2 is the same.
3 u - 16 = 2 u + 20
3 u - 2 u = 20 + 16
1 u = 36
Amount that Gabriel has
= 2 u + 20
= 2 x 36 + 20
= 72 + 20
= $92
(b)
Amount that Shannon has
= 1 u + 16
= 36 + 16
= $52
Answer(s): (a) $92; (b) $52
