Opal has some candy canes and lollipops. If she packs a candy cane and a lollipop in each bag, there will be 20 lollipops left. If she packs 5 candy canes and 6 lollipops in each bag, there will be 29 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 + 20 |
5 p + 29 |
6 p |
Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
After |
0 |
20 |
29 |
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 + 29 --- (1)
1 u + 20 = 6 p
1 u = 6 p - 20 --- (2)
(2) = (1)
6 p - 20 = 5 p + 29
6 p - 5 p = 29 + 20
1 p = 49
Total number of candy canes and lollipops
= (5 p + 29) + 6 p
= 11 p + 29
= 11 x 49 + 29
= 539 + 29
= 568
Answer(s): 568