Winnie has some sweets and mini cupcakes. If she packs a sweet and a mini cupcake in each bag, there will be 27 mini cupcakes left. If she packs 3 sweets and 4 mini cupcakes in each bag, there will be 29 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 + 27 |
3 p + 29 |
4 p |
| Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
| After |
0 |
27 |
29 |
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 = 3 p + 29 --- (1)
1 u + 27 = 4 p
1 u = 4 p - 27 --- (2)
(2) = (1)
4 p - 27 = 3 p + 29
4 p - 3 p = 29 + 27
1 p = 56
Total number of sweets and mini cupcakes
= (3 p + 29) + 4 p
= 7 p + 29
= 7 x 56 + 29
= 392 + 29
= 421
Answer(s): 421
