Perry and Lucy has some money each. If Lucy gives Perry $13, he will have 7 times as much money as her. If Perry gives Lucy $18, he will have the same amount of money as her. How much money does each person have respectively?
- Perry?
- Lucy?
|
Case 1 |
Case 2 |
|
Perry |
Lucy |
Perry |
Lucy |
Before |
7 u - 13 |
1 u + 13 |
4 u + 18 |
4 u - 18 |
Change |
+ 13 |
- 13 |
- 18 |
+ 18 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Lucy gives Perry some money or Perry gives Lucy some money, the total amount of money remains the same.
Total amount that Perry and Lucy have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Perry and Lucy each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Perry has at first in Case 1 and Case 2 is the same.
7 u - 13 = 4 u + 18
7 u - 4 u = 18 + 13
1 u = 31
Amount that Perry has
= 4 u + 18
= 4 x 31 + 18
= 124 + 18
= $142
(b)
Amount that Lucy has
= 1 u + 13
= 31 + 13
= $44
Answer(s): (a) $142; (b) $44