Charlie and Yoko has some money each. If Yoko gives Charlie $19, he will have 7 times as much money as her. If Charlie gives Yoko $15, he will have the same amount of money as her. How much money does each person have respectively?
- Charlie?
- Yoko?
| |
Case 1 |
Case 2 |
| |
Charlie |
Yoko |
Charlie |
Yoko |
| Before |
7 u - 19 |
1 u + 19 |
4 u + 15 |
4 u - 15 |
| Change |
+ 19 |
- 19 |
- 15 |
+ 15 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Yoko gives Charlie some money or Charlie gives Yoko some money, the total amount of money remains the same.
Total amount that Charlie and Yoko have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Charlie and Yoko each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Charlie has at first in Case 1 and Case 2 is the same.
7 u - 19 = 4 u + 15
7 u - 4 u = 15 + 19
1 u = 34
Amount that Charlie has
= 4 u + 15
= 4 x 34 + 15
= 136 + 15
= $151
(b)
Amount that Yoko has
= 1 u + 19
= 34 + 19
= $53
Answer(s): (a) $151; (b) $53
