If Esther gives Jack $15, the amount of money she has will be 75% of his. If Jack gives Esther $8, he will have the same amount of money as her. How much money did each of them have?
(a) Jack
(b) Esther
|
Case 1 |
Case 2 |
|
Jack |
Esther |
Jack |
Esther |
Before |
4 u - 15 |
3 u + 15 |
3.5 u + 8 |
3.5 u - 8 |
Change |
+ 15 |
- 15 |
- 8 |
+ 8 |
After |
4 u |
3 u |
3.5 u |
3.5 u |
(a)
75% =
75100 =
34 In Case 1, when Esther gives to Jack, there is an internal transfer of money from Esther to Jack. The total amount that both have remains the same.
In Case 2, when Jack gives to Esther, there is an internal transfer of money from Jack to Esther. 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 Esther and Jack have
= 4 u + 3 u
= 7 u
Amount that Esther and Jack each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Jack has at first is the same in Case 1 and Case 2.
4 u - 15 = 3.5 u + 8
4 u - 3.5 u = 8 + 15
0.5 u = 23
1 u = 23 ÷ 0.5 = 46
Amount that Jack has
= 4 u - 15
= 4 x 46 - 15
= 184 - 15
= $169
(b)
Amount that Esther has
= 3 u + 15
= 3 x 46 + 15
= 138 + 15
= $153
Answer(s): (a) $169; (b) $153