Zoe has some sweets and candy canes. If she packs a sweet and a candy cane in each bag, there will be 24 candy canes left. If she packs 5 sweets and 6 candy canes in each bag, there will be 20 sweets left. How many sweets and candy canes does she have in all?
| |
Case 1 |
Case 2 |
| |
Sweets |
Candy Canes |
Sweets |
Candy Canes |
| Before |
1 u |
1 u + 24 |
5 p + 20 |
6 p |
| Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
| After |
0 |
24 |
20 |
0 |
The number of sweets at first is the same for Case 1 and 2.
The number of candy canes at first is also the same for Case 1 and 2.
1 u = 5 p + 20 --- (1)
1 u + 24 = 6 p
1 u = 6 p - 24 --- (2)
(2) = (1)
6 p - 24 = 5 p + 20
6 p - 5 p = 20 + 24
1 p = 44
Total number of sweets and candy canes
= (5 p + 20) + 6 p
= 11 p + 20
= 11 x 44 + 20
= 484 + 20
= 504
Answer(s): 504
