If Rachel gives John $15, the amount of money she has will be 30% of his. If John gives Rachel $153, he will have the same amount of money as her. How much money did each of them have?
(a) John
(b) Rachel
|
Case 1 |
Case 2 |
|
John |
Rachel |
John |
Rachel |
Before |
10 u - 15 |
3 u + 15 |
6.5 u + 153 |
6.5 u - 153 |
Change |
+ 15 |
- 15 |
- 153 |
+ 153 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Rachel gives to John, there is an internal transfer of money from Rachel to John. The total amount that both have remains the same.
In Case 2, when John gives to Rachel, there is an internal transfer of money from John to Rachel. 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 Rachel and John have
= 10 u + 3 u
= 13 u
Amount that Rachel and John each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that John has at first is the same in Case 1 and Case 2.
10 u - 15 = 6.5 u + 153
10 u - 6.5 u = 153 + 15
3.5 u = 168
1 u = 168 ÷ 3.5 = 48
Amount that John has
= 10 u - 15
= 10 x 48 - 15
= 480 - 15
= $465
(b)
Amount that Rachel has
= 3 u + 15
= 3 x 48 + 15
= 144 + 15
= $159
Answer(s): (a) $465; (b) $159