Lucy has some sweets and mini cupcakes. If she packs a sweet and a mini cupcake in each bag, there will be 30 mini cupcakes left. If she packs 2 sweets and 3 mini cupcakes in each bag, there will be 20 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 + 30 |
2 p + 20 |
3 p |
Change |
- 1 u |
- 1 u |
- 2 p |
- 3 p |
After |
0 |
30 |
20 |
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 = 2 p + 20 --- (1)
1 u + 30 = 3 p
1 u = 3 p - 30 --- (2)
(2) = (1)
3 p - 30 = 2 p + 20
3 p - 2 p = 20 + 30
1 p = 50
Total number of sweets and mini cupcakes
= (2 p + 20) + 3 p
= 5 p + 20
= 5 x 50 + 20
= 250 + 20
= 270
Answer(s): 270