Fanny has some mini cupcakes and sweets. If she packs a mini cupcake and a sweet in each bag, there will be 25 sweets left. If she packs 4 mini cupcakes and 5 sweets in each bag, there will be 18 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 + 25 |
4 p + 18 |
5 p |
| Change |
- 1 u |
- 1 u |
- 4 p |
- 5 p |
| After |
0 |
25 |
18 |
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 + 18 --- (1)
1 u + 25 = 5 p
1 u = 5 p - 25 --- (2)
(2) = (1)
5 p - 25 = 4 p + 18
5 p - 4 p = 18 + 25
1 p = 43
Total number of mini cupcakes and sweets
= (4 p + 18) + 5 p
= 9 p + 18
= 9 x 43 + 18
= 387 + 18
= 405
Answer(s): 405
