Zara has some lollipops and candy canes. If she packs a lollipop and a candy cane in each bag, there will be 20 candy canes left. If she packs 2 lollipops and 3 candy canes in each bag, there will be 21 lollipops left. How many lollipops and candy canes does she have in all?
| |
Case 1 |
Case 2 |
| |
Lollipops |
Candy Canes |
Lollipops |
Candy Canes |
| Before |
1 u |
1 u + 20 |
2 p + 21 |
3 p |
| Change |
- 1 u |
- 1 u |
- 2 p |
- 3 p |
| After |
0 |
20 |
21 |
0 |
The number of lollipops at first is the same for Case 1 and 2.
The number of candy canes at first is also the same for Case 1 and 2.
1 u = 2 p + 21 --- (1)
1 u + 20 = 3 p
1 u = 3 p - 20 --- (2)
(2) = (1)
3 p - 20 = 2 p + 21
3 p - 2 p = 21 + 20
1 p = 41
Total number of lollipops and candy canes
= (2 p + 21) + 3 p
= 5 p + 21
= 5 x 41 + 21
= 205 + 21
= 226
Answer(s): 226
