If Joelle gives Simon $32, the amount of money she has will be 40% of his. If Simon gives Joelle $19, he will have the same amount of money as her. How much money did each of them have?
(a) Simon
(b) Joelle
|
Case 1 |
Case 2 |
|
Simon |
Joelle |
Simon |
Joelle |
Before |
5 u - 32 |
2 u + 32 |
3.5 u + 19 |
3.5 u - 19 |
Change |
+ 32 |
- 32 |
- 19 |
+ 19 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Joelle gives to Simon, there is an internal transfer of money from Joelle to Simon. The total amount that both have remains the same.
In Case 2, when Simon gives to Joelle, there is an internal transfer of money from Simon to Joelle. 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 Joelle and Simon have
= 5 u + 2 u
= 7 u
Amount that Joelle and Simon each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Simon has at first is the same in Case 1 and Case 2.
5 u - 32 = 3.5 u + 19
5 u - 3.5 u = 19 + 32
1.5 u = 51
1 u = 51 ÷ 1.5 = 34
Amount that Simon has
= 5 u - 32
= 5 x 34 - 32
= 170 - 32
= $138
(b)
Amount that Joelle has
= 2 u + 32
= 2 x 34 + 32
= 68 + 32
= $100
Answer(s): (a) $138; (b) $100