Michael and Emily has some money each. If Emily gives Michael $14, he will have 7 times as much money as her. If Michael gives Emily $17, he will have the same amount of money as her. How much money does each person have respectively?
- Michael?
- Emily?
| |
Case 1 |
Case 2 |
| |
Michael |
Emily |
Michael |
Emily |
| Before |
7 u - 14 |
1 u + 14 |
4 u + 17 |
4 u - 17 |
| Change |
+ 14 |
- 14 |
- 17 |
+ 17 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Emily gives Michael some money or Michael gives Emily some money, the total amount of money remains the same.
Total amount that Michael and Emily have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Michael and Emily each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Michael has at first in Case 1 and Case 2 is the same.
7 u - 14 = 4 u + 17
7 u - 4 u = 17 + 14
1 u = 31
Amount that Michael has
= 4 u + 17
= 4 x 31 + 17
= 124 + 17
= $141
(b)
Amount that Emily has
= 1 u + 14
= 31 + 14
= $45
Answer(s): (a) $141; (b) $45
