Cathy has some mini cupcakes and sweets. If she packs a mini cupcake and a sweet in each bag, there will be 12 sweets left. If she packs 4 mini cupcakes and 5 sweets in each bag, there will be 24 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 + 12 |
4 p + 24 |
5 p |
| Change |
- 1 u |
- 1 u |
- 4 p |
- 5 p |
| After |
0 |
12 |
24 |
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 = 4 p + 24 --- (1)
1 u + 12 = 5 p
1 u = 5 p - 12 --- (2)
(2) = (1)
5 p - 12 = 4 p + 24
5 p - 4 p = 24 + 12
1 p = 36
Total number of mini cupcakes and sweets
= (4 p + 24) + 5 p
= 9 p + 24
= 9 x 36 + 24
= 324 + 24
= 348
Answer(s): 348
