Elyse has some mini cupcakes and lollipops. If she packs a mini cupcake and a lollipop in each bag, there will be 19 lollipops left. If she packs 5 mini cupcakes and 6 lollipops in each bag, there will be 13 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 + 19 |
5 p + 13 |
6 p |
| Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
| After |
0 |
19 |
13 |
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 = 5 p + 13 --- (1)
1 u + 19 = 6 p
1 u = 6 p - 19 --- (2)
(2) = (1)
6 p - 19 = 5 p + 13
6 p - 5 p = 13 + 19
1 p = 32
Total number of mini cupcakes and lollipops
= (5 p + 13) + 6 p
= 11 p + 13
= 11 x 32 + 13
= 352 + 13
= 365
Answer(s): 365
