Jaslyn has some lollipops and caramel apples. If she packs a lollipop and a caramel apple in each bag, there will be 13 caramel apples left. If she packs 5 lollipops and 6 caramel apples in each bag, there will be 11 lollipops left. How many lollipops and caramel apples does she have in all?
| |
Case 1 |
Case 2 |
| |
Lollipops |
Caramel Apples |
Lollipops |
Caramel Apples |
| Before |
1 u |
1 u + 13 |
5 p + 11 |
6 p |
| Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
| After |
0 |
13 |
11 |
0 |
The number of lollipops at first is the same for Case 1 and 2.
The number of caramel apples at first is also the same for Case 1 and 2.
1 u = 5 p + 11 --- (1)
1 u + 13 = 6 p
1 u = 6 p - 13 --- (2)
(2) = (1)
6 p - 13 = 5 p + 11
6 p - 5 p = 11 + 13
1 p = 24
Total number of lollipops and caramel apples
= (5 p + 11) + 6 p
= 11 p + 11
= 11 x 24 + 11
= 264 + 11
= 275
Answer(s): 275
