Vincent and Emily has some money each. If Emily gives Vincent $16, he will have 7 times as much money as her. If Vincent gives Emily $15, he will have the same amount of money as her. How much money does each person have respectively?
- Vincent?
- Emily?
| |
Case 1 |
Case 2 |
| |
Vincent |
Emily |
Vincent |
Emily |
| Before |
7 u - 16 |
1 u + 16 |
4 u + 15 |
4 u - 15 |
| Change |
+ 16 |
- 16 |
- 15 |
+ 15 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Emily gives Vincent some money or Vincent gives Emily some money, the total amount of money remains the same.
Total amount that Vincent and Emily have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Vincent and Emily each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Vincent has at first in Case 1 and Case 2 is the same.
7 u - 16 = 4 u + 15
7 u - 4 u = 15 + 16
1 u = 31
Amount that Vincent has
= 4 u + 15
= 4 x 31 + 15
= 124 + 15
= $139
(b)
Amount that Emily has
= 1 u + 16
= 31 + 16
= $47
Answer(s): (a) $139; (b) $47
