Emily 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 3 sweets and 4 candy canes in each bag, there will be 30 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 |
3 p + 30 |
4 p |
| Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
| After |
0 |
24 |
30 |
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 = 3 p + 30 --- (1)
1 u + 24 = 4 p
1 u = 4 p - 24 --- (2)
(2) = (1)
4 p - 24 = 3 p + 30
4 p - 3 p = 30 + 24
1 p = 54
Total number of sweets and candy canes
= (3 p + 30) + 4 p
= 7 p + 30
= 7 x 54 + 30
= 378 + 30
= 408
Answer(s): 408
