Ivan and Sabrina has some money each. If Sabrina gives Ivan $15, he will have 5 times as much money as her. If Ivan gives Sabrina $14, he will have the same amount of money as her. How much money does each person have respectively?
- Ivan?
- Sabrina?
| |
Case 1 |
Case 2 |
| |
Ivan |
Sabrina |
Ivan |
Sabrina |
| Before |
5 u - 15 |
1 u + 15 |
3 u + 14 |
3 u - 14 |
| Change |
+ 15 |
- 15 |
- 14 |
+ 14 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Sabrina gives Ivan some money or Ivan gives Sabrina some money, the total amount of money remains the same.
Total amount that Ivan and Sabrina have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Ivan and Sabrina each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Ivan has at first in Case 1 and Case 2 is the same.
5 u - 15 = 3 u + 14
5 u - 3 u = 14 + 15
1 u = 29
Amount that Ivan has
= 3 u + 14
= 3 x 29 + 14
= 87 + 14
= $101
(b)
Amount that Sabrina has
= 1 u + 15
= 29 + 15
= $44
Answer(s): (a) $101; (b) $44
