If Usha gives Ryan $19, the amount of money she has will be 10% of his. If Ryan gives Usha $116, he will have the same amount of money as her. How much money did each of them have?
(a) Ryan
(b) Usha
|
Case 1 |
Case 2 |
|
Ryan |
Usha |
Ryan |
Usha |
Before |
10 u - 19 |
1 u + 19 |
5.5 u + 116 |
5.5 u - 116 |
Change |
+ 19 |
- 19 |
- 116 |
+ 116 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Usha gives to Ryan, there is an internal transfer of money from Usha to Ryan. The total amount that both have remains the same.
In Case 2, when Ryan gives to Usha, there is an internal transfer of money from Ryan to Usha. 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 Usha and Ryan have
= 10 u + 1 u
= 11 u
Amount that Usha 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 - 19 = 5.5 u + 116
10 u - 5.5 u = 116 + 19
4.5 u = 135
1 u = 135 ÷ 4.5 = 30
Amount that Ryan has
= 10 u - 19
= 10 x 30 - 19
= 300 - 19
= $281
(b)
Amount that Usha has
= 1 u + 19
= 1 x 30 + 19
= 30 + 19
= $49
Answer(s): (a) $281; (b) $49