Olivia has some candy canes and caramel apples. If she packs a candy cane and a caramel apple in each bag, there will be 27 caramel apples left. If she packs 2 candy canes and 3 caramel apples in each bag, there will be 22 candy canes left. How many candy canes and caramel apples does she have in all?
|
Case 1 |
Case 2 |
|
Candy Canes |
Caramel Apples |
Candy Canes |
Caramel Apples |
Before |
1 u |
1 u + 27 |
2 p + 22 |
3 p |
Change |
- 1 u |
- 1 u |
- 2 p |
- 3 p |
After |
0 |
27 |
22 |
0 |
The number of candy canes at first is the same for Case 1 and 2.
The number of caramel apples at first is also the same for Case 1 and 2.
1 u = 2 p + 22 --- (1)
1 u + 27 = 3 p
1 u = 3 p - 27 --- (2)
(2) = (1)
3 p - 27 = 2 p + 22
3 p - 2 p = 22 + 27
1 p = 49
Total number of candy canes and caramel apples
= (2 p + 22) + 3 p
= 5 p + 22
= 5 x 49 + 22
= 245 + 22
= 267
Answer(s): 267