If Tina gives Sean $30, the amount of money she has will be 30% of his. If Sean gives Tina $131, he will have the same amount of money as her. How much money did each of them have?
(a) Sean
(b) Tina
|
Case 1 |
Case 2 |
|
Sean |
Tina |
Sean |
Tina |
Before |
10 u - 30 |
3 u + 30 |
6.5 u + 131 |
6.5 u - 131 |
Change |
+ 30 |
- 30 |
- 131 |
+ 131 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Tina gives to Sean, there is an internal transfer of money from Tina to Sean. The total amount that both have remains the same.
In Case 2, when Sean gives to Tina, there is an internal transfer of money from Sean to Tina. 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 Tina and Sean have
= 10 u + 3 u
= 13 u
Amount that Tina and Sean each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Sean has at first is the same in Case 1 and Case 2.
10 u - 30 = 6.5 u + 131
10 u - 6.5 u = 131 + 30
3.5 u = 161
1 u = 161 ÷ 3.5 = 46
Amount that Sean has
= 10 u - 30
= 10 x 46 - 30
= 460 - 30
= $430
(b)
Amount that Tina has
= 3 u + 30
= 3 x 46 + 30
= 138 + 30
= $168
Answer(s): (a) $430; (b) $168