Kylie has some candy canes and sweets. If she packs a candy cane and a sweet in each bag, there will be 25 sweets left. If she packs 2 candy canes and 3 sweets in each bag, there will be 24 candy canes left. How many candy canes and sweets does she have in all?
| |
Case 1 |
Case 2 |
| |
Candy Canes |
Sweets |
Candy Canes |
Sweets |
| Before |
1 u |
1 u + 25 |
2 p + 24 |
3 p |
| Change |
- 1 u |
- 1 u |
- 2 p |
- 3 p |
| After |
0 |
25 |
24 |
0 |
The number of candy canes at first is the same for Case 1 and 2.
The number of sweets at first is also the same for Case 1 and 2.
1 u = 2 p + 24 --- (1)
1 u + 25 = 3 p
1 u = 3 p - 25 --- (2)
(2) = (1)
3 p - 25 = 2 p + 24
3 p - 2 p = 24 + 25
1 p = 49
Total number of candy canes and sweets
= (2 p + 24) + 3 p
= 5 p + 24
= 5 x 49 + 24
= 245 + 24
= 269
Answer(s): 269
