Kimberly has some sweets and mini cupcakes. If she packs a sweet and a mini cupcake in each bag, there will be 25 mini cupcakes left. If she packs 4 sweets and 5 mini cupcakes in each bag, there will be 15 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 + 25 |
4 p + 15 |
5 p |
| Change |
- 1 u |
- 1 u |
- 4 p |
- 5 p |
| After |
0 |
25 |
15 |
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 = 4 p + 15 --- (1)
1 u + 25 = 5 p
1 u = 5 p - 25 --- (2)
(2) = (1)
5 p - 25 = 4 p + 15
5 p - 4 p = 15 + 25
1 p = 40
Total number of sweets and mini cupcakes
= (4 p + 15) + 5 p
= 9 p + 15
= 9 x 40 + 15
= 360 + 15
= 375
Answer(s): 375
