If Yoko gives Warren $40, the amount of money she has will be 30% of his. If Warren gives Yoko $135, he will have the same amount of money as her. How much money did each of them have?
(a) Warren
(b) Yoko
|
Case 1 |
Case 2 |
|
Warren |
Yoko |
Warren |
Yoko |
Before |
10 u - 40 |
3 u + 40 |
6.5 u + 135 |
6.5 u - 135 |
Change |
+ 40 |
- 40 |
- 135 |
+ 135 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Yoko gives to Warren, there is an internal transfer of money from Yoko to Warren. The total amount that both have remains the same.
In Case 2, when Warren gives to Yoko, there is an internal transfer of money from Warren to Yoko. The total amount that both have remains the same.
The total amount that both have in Case 1 and Case 2 are the same.
Total amount that Yoko and Warren have
= 10 u + 3 u
= 13 u
Amount that Yoko and Warren each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Warren has at first is the same in Case 1 and Case 2.
10 u - 40 = 6.5 u + 135
10 u - 6.5 u = 135 + 40
3.5 u = 175
1 u = 175 ÷ 3.5 = 50
Amount that Warren has
= 10 u - 40
= 10 x 50 - 40
= 500 - 40
= $460
(b)
Amount that Yoko has
= 3 u + 40
= 3 x 50 + 40
= 150 + 40
= $190
Answer(s): (a) $460; (b) $190