Winnie has some mini cupcakes and lollipops. If she packs a mini cupcake and a lollipop in each bag, there will be 18 lollipops left. If she packs 4 mini cupcakes and 5 lollipops in each bag, there will be 14 mini cupcakes left. How many mini cupcakes and lollipops does she have in all?
| |
Case 1 |
Case 2 |
| |
Mini Cupcakes |
Lollipops |
Mini Cupcakes |
Lollipops |
| Before |
1 u |
1 u + 18 |
4 p + 14 |
5 p |
| Change |
- 1 u |
- 1 u |
- 4 p |
- 5 p |
| After |
0 |
18 |
14 |
0 |
The number of mini cupcakes at first is the same for Case 1 and 2.
The number of lollipops at first is also the same for Case 1 and 2.
1 u = 4 p + 14 --- (1)
1 u + 18 = 5 p
1 u = 5 p - 18 --- (2)
(2) = (1)
5 p - 18 = 4 p + 14
5 p - 4 p = 14 + 18
1 p = 32
Total number of mini cupcakes and lollipops
= (4 p + 14) + 5 p
= 9 p + 14
= 9 x 32 + 14
= 288 + 14
= 302
Answer(s): 302
