Eva has some lollipops and mini cupcakes. If she packs a lollipop and a mini cupcake in each bag, there will be 30 mini cupcakes left. If she packs 3 lollipops and 4 mini cupcakes in each bag, there will be 15 lollipops left. How many lollipops and mini cupcakes does she have in all?
| |
Case 1 |
Case 2 |
| |
Lollipops |
Mini Cupcakes |
Lollipops |
Mini Cupcakes |
| Before |
1 u |
1 u + 30 |
3 p + 15 |
4 p |
| Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
| After |
0 |
30 |
15 |
0 |
The number of lollipops 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 + 15 --- (1)
1 u + 30 = 4 p
1 u = 4 p - 30 --- (2)
(2) = (1)
4 p - 30 = 3 p + 15
4 p - 3 p = 15 + 30
1 p = 45
Total number of lollipops and mini cupcakes
= (3 p + 15) + 4 p
= 7 p + 15
= 7 x 45 + 15
= 315 + 15
= 330
Answer(s): 330
