Kylie has some candy canes and lollipops. If she packs a candy cane and a lollipop in each bag, there will be 12 lollipops left. If she packs 5 candy canes and 6 lollipops in each bag, there will be 22 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 + 12 |
5 p + 22 |
6 p |
| Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
| After |
0 |
12 |
22 |
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 + 22 --- (1)
1 u + 12 = 6 p
1 u = 6 p - 12 --- (2)
(2) = (1)
6 p - 12 = 5 p + 22
6 p - 5 p = 22 + 12
1 p = 34
Total number of candy canes and lollipops
= (5 p + 22) + 6 p
= 11 p + 22
= 11 x 34 + 22
= 374 + 22
= 396
Answer(s): 396
