Julian and Opal has some money each. If Opal gives Julian $11, he will have 3 times as much money as her. If Julian gives Opal $14, he will have the same amount of money as her. How much money does each person have respectively?
- Julian?
- Opal?
| |
Case 1 |
Case 2 |
| |
Julian |
Opal |
Julian |
Opal |
| Before |
3 u - 11 |
1 u + 11 |
2 u + 14 |
2 u - 14 |
| Change |
+ 11 |
- 11 |
- 14 |
+ 14 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Opal gives Julian some money or Julian gives Opal some money, the total amount of money remains the same.
Total amount that Julian and Opal have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Julian and Opal each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Julian has at first in Case 1 and Case 2 is the same.
3 u - 11 = 2 u + 14
3 u - 2 u = 14 + 11
1 u = 25
Amount that Julian has
= 2 u + 14
= 2 x 25 + 14
= 50 + 14
= $64
(b)
Amount that Opal has
= 1 u + 11
= 25 + 11
= $36
Answer(s): (a) $64; (b) $36
