Ian and Nora has some money each. If Nora gives Ian $13, he will have 3 times as much money as her. If Ian gives Nora $10, he will have the same amount of money as her. How much money does each person have respectively?
- Ian?
- Nora?
|
Case 1 |
Case 2 |
|
Ian |
Nora |
Ian |
Nora |
Before |
3 u - 13 |
1 u + 13 |
2 u + 10 |
2 u - 10 |
Change |
+ 13 |
- 13 |
- 10 |
+ 10 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Nora gives Ian some money or Ian gives Nora some money, the total amount of money remains the same.
Total amount that Ian and Nora have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Ian and Nora each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Ian has at first in Case 1 and Case 2 is the same.
3 u - 13 = 2 u + 10
3 u - 2 u = 10 + 13
1 u = 23
Amount that Ian has
= 2 u + 10
= 2 x 23 + 10
= 46 + 10
= $56
(b)
Amount that Nora has
= 1 u + 13
= 23 + 13
= $36
Answer(s): (a) $56; (b) $36