Ian and Usha has some money each. If Usha gives Ian $17, he will have 7 times as much money as her. If Ian gives Usha $11, he will have the same amount of money as her. How much money does each person have respectively?
- Ian?
- Usha?
|
Case 1 |
Case 2 |
|
Ian |
Usha |
Ian |
Usha |
Before |
7 u - 17 |
1 u + 17 |
4 u + 11 |
4 u - 11 |
Change |
+ 17 |
- 17 |
- 11 |
+ 11 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Usha gives Ian some money or Ian gives Usha some money, the total amount of money remains the same.
Total amount that Ian and Usha have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Ian and Usha each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Ian has at first in Case 1 and Case 2 is the same.
7 u - 17 = 4 u + 11
7 u - 4 u = 11 + 17
1 u = 28
Amount that Ian has
= 4 u + 11
= 4 x 28 + 11
= 112 + 11
= $123
(b)
Amount that Usha has
= 1 u + 17
= 28 + 17
= $45
Answer(s): (a) $123; (b) $45