Will and Wendy has some money each. If Wendy gives Will $12, he will have 5 times as much money as her. If Will gives Wendy $18, he will have the same amount of money as her. How much money does each person have respectively?
- Will?
- Wendy?
| |
Case 1 |
Case 2 |
| |
Will |
Wendy |
Will |
Wendy |
| Before |
5 u - 12 |
1 u + 12 |
3 u + 18 |
3 u - 18 |
| Change |
+ 12 |
- 12 |
- 18 |
+ 18 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Wendy gives Will some money or Will gives Wendy some money, the total amount of money remains the same.
Total amount that Will and Wendy have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Will and Wendy each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Will has at first in Case 1 and Case 2 is the same.
5 u - 12 = 3 u + 18
5 u - 3 u = 18 + 12
1 u = 30
Amount that Will has
= 3 u + 18
= 3 x 30 + 18
= 90 + 18
= $108
(b)
Amount that Wendy has
= 1 u + 12
= 30 + 12
= $42
Answer(s): (a) $108; (b) $42
