If Erika gives Ryan $40, the amount of money she has will be 10% of his. If Ryan gives Erika $68, he will have the same amount of money as her. How much money did each of them have?
(a) Ryan
(b) Erika
|
Case 1 |
Case 2 |
|
Ryan |
Erika |
Ryan |
Erika |
Before |
10 u - 40 |
1 u + 40 |
5.5 u + 68 |
5.5 u - 68 |
Change |
+ 40 |
- 40 |
- 68 |
+ 68 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Erika gives to Ryan, there is an internal transfer of money from Erika to Ryan. The total amount that both have remains the same.
In Case 2, when Ryan gives to Erika, there is an internal transfer of money from Ryan to Erika. 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 Erika and Ryan have
= 10 u + 1 u
= 11 u
Amount that Erika 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 - 40 = 5.5 u + 68
10 u - 5.5 u = 68 + 40
4.5 u = 108
1 u = 108 ÷ 4.5 = 24
Amount that Ryan has
= 10 u - 40
= 10 x 24 - 40
= 240 - 40
= $200
(b)
Amount that Erika has
= 1 u + 40
= 1 x 24 + 40
= 24 + 40
= $64
Answer(s): (a) $200; (b) $64