If Tina gives Ivan $26, the amount of money she has will be 10% of his. If Ivan gives Tina $163, he will have the same amount of money as her. How much money did each of them have?
(a) Ivan
(b) Tina
|
Case 1 |
Case 2 |
|
Ivan |
Tina |
Ivan |
Tina |
Before |
10 u - 26 |
1 u + 26 |
5.5 u + 163 |
5.5 u - 163 |
Change |
+ 26 |
- 26 |
- 163 |
+ 163 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Tina gives to Ivan, there is an internal transfer of money from Tina to Ivan. The total amount that both have remains the same.
In Case 2, when Ivan gives to Tina, there is an internal transfer of money from Ivan 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 Ivan have
= 10 u + 1 u
= 11 u
Amount that Tina and Ivan each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that Ivan has at first is the same in Case 1 and Case 2.
10 u - 26 = 5.5 u + 163
10 u - 5.5 u = 163 + 26
4.5 u = 189
1 u = 189 ÷ 4.5 = 42
Amount that Ivan has
= 10 u - 26
= 10 x 42 - 26
= 420 - 26
= $394
(b)
Amount that Tina has
= 1 u + 26
= 1 x 42 + 26
= 42 + 26
= $68
Answer(s): (a) $394; (b) $68