If Sarah gives Ryan $33, the amount of money she has will be 10% of his. If Ryan gives Sarah $138, he will have the same amount of money as her. How much money did each of them have?
(a) Ryan
(b) Sarah
|
Case 1 |
Case 2 |
|
Ryan |
Sarah |
Ryan |
Sarah |
Before |
10 u - 33 |
1 u + 33 |
5.5 u + 138 |
5.5 u - 138 |
Change |
+ 33 |
- 33 |
- 138 |
+ 138 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Sarah gives to Ryan, there is an internal transfer of money from Sarah to Ryan. The total amount that both have remains the same.
In Case 2, when Ryan gives to Sarah, there is an internal transfer of money from Ryan 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 Ryan have
= 10 u + 1 u
= 11 u
Amount that Sarah and Ryan each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that Ryan has at first is the same in Case 1 and Case 2.
10 u - 33 = 5.5 u + 138
10 u - 5.5 u = 138 + 33
4.5 u = 171
1 u = 171 ÷ 4.5 = 38
Amount that Ryan has
= 10 u - 33
= 10 x 38 - 33
= 380 - 33
= $347
(b)
Amount that Sarah has
= 1 u + 33
= 1 x 38 + 33
= 38 + 33
= $71
Answer(s): (a) $347; (b) $71