Tiffany has some lollipops and mini cupcakes. If she packs a lollipop and a mini cupcake in each bag, there will be 27 mini cupcakes left. If she packs 4 lollipops and 5 mini cupcakes in each bag, there will be 18 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 + 27 |
4 p + 18 |
5 p |
| Change |
- 1 u |
- 1 u |
- 4 p |
- 5 p |
| After |
0 |
27 |
18 |
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 = 4 p + 18 --- (1)
1 u + 27 = 5 p
1 u = 5 p - 27 --- (2)
(2) = (1)
5 p - 27 = 4 p + 18
5 p - 4 p = 18 + 27
1 p = 45
Total number of lollipops and mini cupcakes
= (4 p + 18) + 5 p
= 9 p + 18
= 9 x 45 + 18
= 405 + 18
= 423
Answer(s): 423
