Billy and Nora has some money each. If Nora gives Billy $18, he will have 5 times as much money as her. If Billy gives Nora $12, he will have the same amount of money as her. How much money does each person have respectively?
- Billy?
- Nora?
| |
Case 1 |
Case 2 |
| |
Billy |
Nora |
Billy |
Nora |
| Before |
5 u - 18 |
1 u + 18 |
3 u + 12 |
3 u - 12 |
| Change |
+ 18 |
- 18 |
- 12 |
+ 12 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Nora gives Billy some money or Billy gives Nora some money, the total amount of money remains the same.
Total amount that Billy and Nora have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Billy and Nora each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Billy has at first in Case 1 and Case 2 is the same.
5 u - 18 = 3 u + 12
5 u - 3 u = 12 + 18
1 u = 30
Amount that Billy has
= 3 u + 12
= 3 x 30 + 12
= 90 + 12
= $102
(b)
Amount that Nora has
= 1 u + 18
= 30 + 18
= $48
Answer(s): (a) $102; (b) $48
