Vanessa has some lollipops and mini cupcakes. If she packs a lollipop and a mini cupcake in each bag, there will be 13 mini cupcakes left. If she packs 2 lollipops and 3 mini cupcakes in each bag, there will be 23 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 + 13 |
2 p + 23 |
3 p |
| Change |
- 1 u |
- 1 u |
- 2 p |
- 3 p |
| After |
0 |
13 |
23 |
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 = 2 p + 23 --- (1)
1 u + 13 = 3 p
1 u = 3 p - 13 --- (2)
(2) = (1)
3 p - 13 = 2 p + 23
3 p - 2 p = 23 + 13
1 p = 36
Total number of lollipops and mini cupcakes
= (2 p + 23) + 3 p
= 5 p + 23
= 5 x 36 + 23
= 180 + 23
= 203
Answer(s): 203
