Opal has some mini cupcakes and sweets. If she packs a mini cupcake and a sweet in each bag, there will be 30 sweets left. If she packs 5 mini cupcakes and 6 sweets in each bag, there will be 19 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 + 30 |
5 p + 19 |
6 p |
Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
After |
0 |
30 |
19 |
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 = 5 p + 19 --- (1)
1 u + 30 = 6 p
1 u = 6 p - 30 --- (2)
(2) = (1)
6 p - 30 = 5 p + 19
6 p - 5 p = 19 + 30
1 p = 49
Total number of mini cupcakes and sweets
= (5 p + 19) + 6 p
= 11 p + 19
= 11 x 49 + 19
= 539 + 19
= 558
Answer(s): 558