Charlie and Lucy has some money each. If Lucy gives Charlie $12, he will have 5 times as much money as her. If Charlie gives Lucy $15, he will have the same amount of money as her. How much money does each person have respectively?
- Charlie?
- Lucy?
| |
Case 1 |
Case 2 |
| |
Charlie |
Lucy |
Charlie |
Lucy |
| Before |
5 u - 12 |
1 u + 12 |
3 u + 15 |
3 u - 15 |
| Change |
+ 12 |
- 12 |
- 15 |
+ 15 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Lucy gives Charlie some money or Charlie gives Lucy some money, the total amount of money remains the same.
Total amount that Charlie and Lucy have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Charlie and Lucy each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Charlie has at first in Case 1 and Case 2 is the same.
5 u - 12 = 3 u + 15
5 u - 3 u = 15 + 12
1 u = 27
Amount that Charlie has
= 3 u + 15
= 3 x 27 + 15
= 81 + 15
= $96
(b)
Amount that Lucy has
= 1 u + 12
= 27 + 12
= $39
Answer(s): (a) $96; (b) $39
