Sean and Wendy has some money each. If Wendy gives Sean $18, he will have 3 times as much money as her. If Sean gives Wendy $15, he will have the same amount of money as her. How much money does each person have respectively?
- Sean?
- Wendy?
| |
Case 1 |
Case 2 |
| |
Sean |
Wendy |
Sean |
Wendy |
| Before |
3 u - 18 |
1 u + 18 |
2 u + 15 |
2 u - 15 |
| Change |
+ 18 |
- 18 |
- 15 |
+ 15 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Wendy gives Sean some money or Sean gives Wendy some money, the total amount of money remains the same.
Total amount that Sean and Wendy have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Sean and Wendy each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Sean has at first in Case 1 and Case 2 is the same.
3 u - 18 = 2 u + 15
3 u - 2 u = 15 + 18
1 u = 33
Amount that Sean has
= 2 u + 15
= 2 x 33 + 15
= 66 + 15
= $81
(b)
Amount that Wendy has
= 1 u + 18
= 33 + 18
= $51
Answer(s): (a) $81; (b) $51
