Nicole has some mini cupcakes and sweets. If she packs a mini cupcake and a sweet in each bag, there will be 13 sweets left. If she packs 5 mini cupcakes and 6 sweets in each bag, there will be 14 mini cupcakes left. How many mini cupcakes and sweets does she have in all?
| |
Case 1 |
Case 2 |
| |
Mini Cupcakes |
Sweets |
Mini Cupcakes |
Sweets |
| Before |
1 u |
1 u + 13 |
5 p + 14 |
6 p |
| Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
| After |
0 |
13 |
14 |
0 |
The number of mini cupcakes 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 = 5 p + 14 --- (1)
1 u + 13 = 6 p
1 u = 6 p - 13 --- (2)
(2) = (1)
6 p - 13 = 5 p + 14
6 p - 5 p = 14 + 13
1 p = 27
Total number of mini cupcakes and sweets
= (5 p + 14) + 6 p
= 11 p + 14
= 11 x 27 + 14
= 297 + 14
= 311
Answer(s): 311
