If Barbara gives Cole $18, the amount of money she has will be 30% of his. If Cole gives Barbara $115, he will have the same amount of money as her. How much money did each of them have?
(a) Cole
(b) Barbara
|
Case 1 |
Case 2 |
|
Cole |
Barbara |
Cole |
Barbara |
Before |
10 u - 18 |
3 u + 18 |
6.5 u + 115 |
6.5 u - 115 |
Change |
+ 18 |
- 18 |
- 115 |
+ 115 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Barbara gives to Cole, there is an internal transfer of money from Barbara to Cole. The total amount that both have remains the same.
In Case 2, when Cole gives to Barbara, there is an internal transfer of money from Cole to Barbara. 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 Barbara and Cole have
= 10 u + 3 u
= 13 u
Amount that Barbara and Cole each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Cole has at first is the same in Case 1 and Case 2.
10 u - 18 = 6.5 u + 115
10 u - 6.5 u = 115 + 18
3.5 u = 133
1 u = 133 ÷ 3.5 = 38
Amount that Cole has
= 10 u - 18
= 10 x 38 - 18
= 380 - 18
= $362
(b)
Amount that Barbara has
= 3 u + 18
= 3 x 38 + 18
= 114 + 18
= $132
Answer(s): (a) $362; (b) $132