Cathy has some mini cupcakes and sweets. If she packs a mini cupcake and a sweet in each bag, there will be 27 sweets left. If she packs 3 mini cupcakes and 4 sweets in each bag, there will be 17 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 + 27 |
3 p + 17 |
4 p |
| Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
| After |
0 |
27 |
17 |
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 = 3 p + 17 --- (1)
1 u + 27 = 4 p
1 u = 4 p - 27 --- (2)
(2) = (1)
4 p - 27 = 3 p + 17
4 p - 3 p = 17 + 27
1 p = 44
Total number of mini cupcakes and sweets
= (3 p + 17) + 4 p
= 7 p + 17
= 7 x 44 + 17
= 308 + 17
= 325
Answer(s): 325
