Michael and Jade has some money each. If Jade gives Michael $12, he will have 5 times as much money as her. If Michael gives Jade $14, he will have the same amount of money as her. How much money does each person have respectively?
- Michael?
- Jade?
|
Case 1 |
Case 2 |
|
Michael |
Jade |
Michael |
Jade |
Before |
5 u - 12 |
1 u + 12 |
3 u + 14 |
3 u - 14 |
Change |
+ 12 |
- 12 |
- 14 |
+ 14 |
After |
5 u |
1 u |
3 u |
3 u |
(a)
If Jade gives Michael some money or Michael gives Jade some money, the total amount of money remains the same.
Total amount that Michael and Jade have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Michael and Jade each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Michael has at first in Case 1 and Case 2 is the same.
5 u - 12 = 3 u + 14
5 u - 3 u = 14 + 12
1 u = 26
Amount that Michael has
= 3 u + 14
= 3 x 26 + 14
= 78 + 14
= $92
(b)
Amount that Jade has
= 1 u + 12
= 26 + 12
= $38
Answer(s): (a) $92; (b) $38