Opal has some candy canes and lollipops. If she packs a candy cane and a lollipop in each bag, there will be 10 lollipops left. If she packs 5 candy canes and 6 lollipops in each bag, there will be 18 candy canes left. How many candy canes and lollipops does she have in all?
| |
Case 1 |
Case 2 |
| |
Candy Canes |
Lollipops |
Candy Canes |
Lollipops |
| Before |
1 u |
1 u + 10 |
5 p + 18 |
6 p |
| Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
| After |
0 |
10 |
18 |
0 |
The number of candy canes 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 + 18 --- (1)
1 u + 10 = 6 p
1 u = 6 p - 10 --- (2)
(2) = (1)
6 p - 10 = 5 p + 18
6 p - 5 p = 18 + 10
1 p = 28
Total number of candy canes and lollipops
= (5 p + 18) + 6 p
= 11 p + 18
= 11 x 28 + 18
= 308 + 18
= 326
Answer(s): 326
