If Xuan gives Cole $23, the amount of money she has will be 40% of his. If Cole gives Xuan $43, he will have the same amount of money as her. How much money did each of them have?
(a) Cole
(b) Xuan
|
Case 1 |
Case 2 |
|
Cole |
Xuan |
Cole |
Xuan |
Before |
5 u - 23 |
2 u + 23 |
3.5 u + 43 |
3.5 u - 43 |
Change |
+ 23 |
- 23 |
- 43 |
+ 43 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Xuan gives to Cole, there is an internal transfer of money from Xuan to Cole. The total amount that both have remains the same.
In Case 2, when Cole gives to Xuan, there is an internal transfer of money from Cole to Xuan. 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 Xuan and Cole have
= 5 u + 2 u
= 7 u
Amount that Xuan and Cole each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Cole has at first is the same in Case 1 and Case 2.
5 u - 23 = 3.5 u + 43
5 u - 3.5 u = 43 + 23
1.5 u = 66
1 u = 66 ÷ 1.5 = 44
Amount that Cole has
= 5 u - 23
= 5 x 44 - 23
= 220 - 23
= $197
(b)
Amount that Xuan has
= 2 u + 23
= 2 x 44 + 23
= 88 + 23
= $111
Answer(s): (a) $197; (b) $111