Gabby has some mini cupcakes and candy canes. If she packs a mini cupcake and a candy cane in each bag, there will be 11 candy canes left. If she packs 2 mini cupcakes and 3 candy canes in each bag, there will be 27 mini cupcakes left. How many mini cupcakes and candy canes does she have in all?
| |
Case 1 |
Case 2 |
| |
Mini Cupcakes |
Candy Canes |
Mini Cupcakes |
Candy Canes |
| Before |
1 u |
1 u + 11 |
2 p + 27 |
3 p |
| Change |
- 1 u |
- 1 u |
- 2 p |
- 3 p |
| After |
0 |
11 |
27 |
0 |
The number of mini cupcakes 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 = 2 p + 27 --- (1)
1 u + 11 = 3 p
1 u = 3 p - 11 --- (2)
(2) = (1)
3 p - 11 = 2 p + 27
3 p - 2 p = 27 + 11
1 p = 38
Total number of mini cupcakes and candy canes
= (2 p + 27) + 3 p
= 5 p + 27
= 5 x 38 + 27
= 190 + 27
= 217
Answer(s): 217
