Eric and Vanessa has some money each. If Vanessa gives Eric $10, he will have 7 times as much money as her. If Eric gives Vanessa $11, he will have the same amount of money as her. How much money does each person have respectively?
- Eric?
- Vanessa?
| |
Case 1 |
Case 2 |
| |
Eric |
Vanessa |
Eric |
Vanessa |
| Before |
7 u - 10 |
1 u + 10 |
4 u + 11 |
4 u - 11 |
| Change |
+ 10 |
- 10 |
- 11 |
+ 11 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Vanessa gives Eric some money or Eric gives Vanessa some money, the total amount of money remains the same.
Total amount that Eric and Vanessa have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Eric and Vanessa each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Eric has at first in Case 1 and Case 2 is the same.
7 u - 10 = 4 u + 11
7 u - 4 u = 11 + 10
1 u = 21
Amount that Eric has
= 4 u + 11
= 4 x 21 + 11
= 84 + 11
= $95
(b)
Amount that Vanessa has
= 1 u + 10
= 21 + 10
= $31
Answer(s): (a) $95; (b) $31
