Zane and Natalie has some money each. If Natalie gives Zane $18, he will have 3 times as much money as her. If Zane gives Natalie $16, he will have the same amount of money as her. How much money does each person have respectively?
- Zane?
- Natalie?
|
Case 1 |
Case 2 |
|
Zane |
Natalie |
Zane |
Natalie |
Before |
3 u - 18 |
1 u + 18 |
2 u + 16 |
2 u - 16 |
Change |
+ 18 |
- 18 |
- 16 |
+ 16 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Natalie gives Zane some money or Zane gives Natalie some money, the total amount of money remains the same.
Total amount that Zane and Natalie have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Zane and Natalie each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Zane has at first in Case 1 and Case 2 is the same.
3 u - 18 = 2 u + 16
3 u - 2 u = 16 + 18
1 u = 34
Amount that Zane has
= 2 u + 16
= 2 x 34 + 16
= 68 + 16
= $84
(b)
Amount that Natalie has
= 1 u + 18
= 34 + 18
= $52
Answer(s): (a) $84; (b) $52