Sean and Winnie has some money each. If Winnie gives Sean $19, he will have 7 times as much money as her. If Sean gives Winnie $12, he will have the same amount of money as her. How much money does each person have respectively?
- Sean?
- Winnie?
| |
Case 1 |
Case 2 |
| |
Sean |
Winnie |
Sean |
Winnie |
| Before |
7 u - 19 |
1 u + 19 |
4 u + 12 |
4 u - 12 |
| Change |
+ 19 |
- 19 |
- 12 |
+ 12 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Winnie gives Sean some money or Sean gives Winnie some money, the total amount of money remains the same.
Total amount that Sean and Winnie have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Sean and Winnie each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Sean has at first in Case 1 and Case 2 is the same.
7 u - 19 = 4 u + 12
7 u - 4 u = 12 + 19
1 u = 31
Amount that Sean has
= 4 u + 12
= 4 x 31 + 12
= 124 + 12
= $136
(b)
Amount that Winnie has
= 1 u + 19
= 31 + 19
= $50
Answer(s): (a) $136; (b) $50
