Fanny has some sweets and mini cupcakes. If she packs a sweet and a mini cupcake in each bag, there will be 14 mini cupcakes left. If she packs 5 sweets and 6 mini cupcakes in each bag, there will be 21 sweets left. How many sweets and mini cupcakes does she have in all?
| |
Case 1 |
Case 2 |
| |
Sweets |
Mini Cupcakes |
Sweets |
Mini Cupcakes |
| Before |
1 u |
1 u + 14 |
5 p + 21 |
6 p |
| Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
| After |
0 |
14 |
21 |
0 |
The number of sweets at first is the same for Case 1 and 2.
The number of mini cupcakes at first is also the same for Case 1 and 2.
1 u = 5 p + 21 --- (1)
1 u + 14 = 6 p
1 u = 6 p - 14 --- (2)
(2) = (1)
6 p - 14 = 5 p + 21
6 p - 5 p = 21 + 14
1 p = 35
Total number of sweets and mini cupcakes
= (5 p + 21) + 6 p
= 11 p + 21
= 11 x 35 + 21
= 385 + 21
= 406
Answer(s): 406
