Pierre and Cathy has some money each. If Cathy gives Pierre $14, he will have 7 times as much money as her. If Pierre gives Cathy $13, he will have the same amount of money as her. How much money does each person have respectively?
- Pierre?
- Cathy?
| |
Case 1 |
Case 2 |
| |
Pierre |
Cathy |
Pierre |
Cathy |
| Before |
7 u - 14 |
1 u + 14 |
4 u + 13 |
4 u - 13 |
| Change |
+ 14 |
- 14 |
- 13 |
+ 13 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Cathy gives Pierre some money or Pierre gives Cathy some money, the total amount of money remains the same.
Total amount that Pierre and Cathy have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Pierre and Cathy each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Pierre has at first in Case 1 and Case 2 is the same.
7 u - 14 = 4 u + 13
7 u - 4 u = 13 + 14
1 u = 27
Amount that Pierre has
= 4 u + 13
= 4 x 27 + 13
= 108 + 13
= $121
(b)
Amount that Cathy has
= 1 u + 14
= 27 + 14
= $41
Answer(s): (a) $121; (b) $41
