If Sarah gives Riordan $23, the amount of money she has will be 30% of his. If Riordan gives Sarah $75, he will have the same amount of money as her. How much money did each of them have?
(a) Riordan
(b) Sarah
|
Case 1 |
Case 2 |
|
Riordan |
Sarah |
Riordan |
Sarah |
Before |
10 u - 23 |
3 u + 23 |
6.5 u + 75 |
6.5 u - 75 |
Change |
+ 23 |
- 23 |
- 75 |
+ 75 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Sarah gives to Riordan, there is an internal transfer of money from Sarah to Riordan. The total amount that both have remains the same.
In Case 2, when Riordan gives to Sarah, there is an internal transfer of money from Riordan to Sarah. 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 Sarah and Riordan have
= 10 u + 3 u
= 13 u
Amount that Sarah and Riordan each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Riordan has at first is the same in Case 1 and Case 2.
10 u - 23 = 6.5 u + 75
10 u - 6.5 u = 75 + 23
3.5 u = 98
1 u = 98 ÷ 3.5 = 28
Amount that Riordan has
= 10 u - 23
= 10 x 28 - 23
= 280 - 23
= $257
(b)
Amount that Sarah has
= 3 u + 23
= 3 x 28 + 23
= 84 + 23
= $107
Answer(s): (a) $257; (b) $107