If Irene gives Julian $23, the amount of money she has will be 10% of his. If Julian gives Irene $157, he will have the same amount of money as her. How much money did each of them have?
(a) Julian
(b) Irene
|
Case 1 |
Case 2 |
|
Julian |
Irene |
Julian |
Irene |
Before |
10 u - 23 |
1 u + 23 |
5.5 u + 157 |
5.5 u - 157 |
Change |
+ 23 |
- 23 |
- 157 |
+ 157 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Irene gives to Julian, there is an internal transfer of money from Irene to Julian. The total amount that both have remains the same.
In Case 2, when Julian gives to Irene, there is an internal transfer of money from Julian to Irene. 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 Irene and Julian have
= 10 u + 1 u
= 11 u
Amount that Irene and Julian each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that Julian has at first is the same in Case 1 and Case 2.
10 u - 23 = 5.5 u + 157
10 u - 5.5 u = 157 + 23
4.5 u = 180
1 u = 180 ÷ 4.5 = 40
Amount that Julian has
= 10 u - 23
= 10 x 40 - 23
= 400 - 23
= $377
(b)
Amount that Irene has
= 1 u + 23
= 1 x 40 + 23
= 40 + 23
= $63
Answer(s): (a) $377; (b) $63