Zane and Emily has some money each. If Emily gives Zane $19, he will have 5 times as much money as her. If Zane gives Emily $12, he will have the same amount of money as her. How much money does each person have respectively?
- Zane?
- Emily?
|
Case 1 |
Case 2 |
|
Zane |
Emily |
Zane |
Emily |
Before |
5 u - 19 |
1 u + 19 |
3 u + 12 |
3 u - 12 |
Change |
+ 19 |
- 19 |
- 12 |
+ 12 |
After |
5 u |
1 u |
3 u |
3 u |
(a)
If Emily gives Zane some money or Zane gives Emily some money, the total amount of money remains the same.
Total amount that Zane and Emily have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Zane and Emily each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Zane has at first in Case 1 and Case 2 is the same.
5 u - 19 = 3 u + 12
5 u - 3 u = 12 + 19
1 u = 31
Amount that Zane has
= 3 u + 12
= 3 x 31 + 12
= 93 + 12
= $105
(b)
Amount that Emily has
= 1 u + 19
= 31 + 19
= $50
Answer(s): (a) $105; (b) $50