Cody and Olivia has some money each. If Olivia gives Cody $17, he will have 3 times as much money as her. If Cody gives Olivia $13, he will have the same amount of money as her. How much money does each person have respectively?
- Cody?
- Olivia?
| |
Case 1 |
Case 2 |
| |
Cody |
Olivia |
Cody |
Olivia |
| Before |
3 u - 17 |
1 u + 17 |
2 u + 13 |
2 u - 13 |
| Change |
+ 17 |
- 17 |
- 13 |
+ 13 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Olivia gives Cody some money or Cody gives Olivia some money, the total amount of money remains the same.
Total amount that Cody and Olivia have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Cody and Olivia each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Cody has at first in Case 1 and Case 2 is the same.
3 u - 17 = 2 u + 13
3 u - 2 u = 13 + 17
1 u = 30
Amount that Cody has
= 2 u + 13
= 2 x 30 + 13
= 60 + 13
= $73
(b)
Amount that Olivia has
= 1 u + 17
= 30 + 17
= $47
Answer(s): (a) $73; (b) $47
