Paul and Elyse has some money each. If Elyse gives Paul $15, he will have 7 times as much money as her. If Paul gives Elyse $13, he will have the same amount of money as her. How much money does each person have respectively?
- Paul?
- Elyse?
|
Case 1 |
Case 2 |
|
Paul |
Elyse |
Paul |
Elyse |
Before |
7 u - 15 |
1 u + 15 |
4 u + 13 |
4 u - 13 |
Change |
+ 15 |
- 15 |
- 13 |
+ 13 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Elyse gives Paul some money or Paul gives Elyse some money, the total amount of money remains the same.
Total amount that Paul and Elyse have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Paul and Elyse each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Paul has at first in Case 1 and Case 2 is the same.
7 u - 15 = 4 u + 13
7 u - 4 u = 13 + 15
1 u = 28
Amount that Paul has
= 4 u + 13
= 4 x 28 + 13
= 112 + 13
= $125
(b)
Amount that Elyse has
= 1 u + 15
= 28 + 15
= $43
Answer(s): (a) $125; (b) $43