If Gem gives Riordan $32, the amount of money she has will be 40% of his. If Riordan gives Gem $4, he will have the same amount of money as her. How much money did each of them have?
(a) Riordan
(b) Gem
|
Case 1 |
Case 2 |
|
Riordan |
Gem |
Riordan |
Gem |
Before |
5 u - 32 |
2 u + 32 |
3.5 u + 4 |
3.5 u - 4 |
Change |
+ 32 |
- 32 |
- 4 |
+ 4 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Gem gives to Riordan, there is an internal transfer of money from Gem to Riordan. The total amount that both have remains the same.
In Case 2, when Riordan gives to Gem, there is an internal transfer of money from Riordan to Gem. 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 Gem and Riordan have
= 5 u + 2 u
= 7 u
Amount that Gem and Riordan each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Riordan has at first is the same in Case 1 and Case 2.
5 u - 32 = 3.5 u + 4
5 u - 3.5 u = 4 + 32
1.5 u = 36
1 u = 36 ÷ 1.5 = 24
Amount that Riordan has
= 5 u - 32
= 5 x 24 - 32
= 120 - 32
= $88
(b)
Amount that Gem has
= 2 u + 32
= 2 x 24 + 32
= 48 + 32
= $80
Answer(s): (a) $88; (b) $80