Vincent and Yoko has some money each. If Yoko gives Vincent $19, he will have 5 times as much money as her. If Vincent gives Yoko $16, he will have the same amount of money as her. How much money does each person have respectively?
- Vincent?
- Yoko?
| |
Case 1 |
Case 2 |
| |
Vincent |
Yoko |
Vincent |
Yoko |
| Before |
5 u - 19 |
1 u + 19 |
3 u + 16 |
3 u - 16 |
| Change |
+ 19 |
- 19 |
- 16 |
+ 16 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Yoko gives Vincent some money or Vincent gives Yoko some money, the total amount of money remains the same.
Total amount that Vincent and Yoko have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Vincent and Yoko each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Vincent has at first in Case 1 and Case 2 is the same.
5 u - 19 = 3 u + 16
5 u - 3 u = 16 + 19
1 u = 35
Amount that Vincent has
= 3 u + 16
= 3 x 35 + 16
= 105 + 16
= $121
(b)
Amount that Yoko has
= 1 u + 19
= 35 + 19
= $54
Answer(s): (a) $121; (b) $54
