Warren and Julie has some money each. If Julie gives Warren $14, he will have 5 times as much money as her. If Warren gives Julie $19, he will have the same amount of money as her. How much money does each person have respectively?
- Warren?
- Julie?
| |
Case 1 |
Case 2 |
| |
Warren |
Julie |
Warren |
Julie |
| Before |
5 u - 14 |
1 u + 14 |
3 u + 19 |
3 u - 19 |
| Change |
+ 14 |
- 14 |
- 19 |
+ 19 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Julie gives Warren some money or Warren gives Julie some money, the total amount of money remains the same.
Total amount that Warren and Julie have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Warren and Julie each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Warren has at first in Case 1 and Case 2 is the same.
5 u - 14 = 3 u + 19
5 u - 3 u = 19 + 14
1 u = 33
Amount that Warren has
= 3 u + 19
= 3 x 33 + 19
= 99 + 19
= $118
(b)
Amount that Julie has
= 1 u + 14
= 33 + 14
= $47
Answer(s): (a) $118; (b) $47
