Julian and Cindy has some money each. If Cindy gives Julian $16, he will have 5 times as much money as her. If Julian gives Cindy $19, he will have the same amount of money as her. How much money does each person have respectively?
- Julian?
- Cindy?
|
Case 1 |
Case 2 |
|
Julian |
Cindy |
Julian |
Cindy |
Before |
5 u - 16 |
1 u + 16 |
3 u + 19 |
3 u - 19 |
Change |
+ 16 |
- 16 |
- 19 |
+ 19 |
After |
5 u |
1 u |
3 u |
3 u |
(a)
If Cindy gives Julian some money or Julian gives Cindy some money, the total amount of money remains the same.
Total amount that Julian and Cindy have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Julian and Cindy each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Julian has at first in Case 1 and Case 2 is the same.
5 u - 16 = 3 u + 19
5 u - 3 u = 19 + 16
1 u = 35
Amount that Julian has
= 3 u + 19
= 3 x 35 + 19
= 105 + 19
= $124
(b)
Amount that Cindy has
= 1 u + 16
= 35 + 16
= $51
Answer(s): (a) $124; (b) $51