Jade has some lollipops and candy canes. If she packs a lollipop and a candy cane in each bag, there will be 30 candy canes left. If she packs 3 lollipops and 4 candy canes in each bag, there will be 19 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 + 30 |
3 p + 19 |
4 p |
| Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
| After |
0 |
30 |
19 |
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 = 3 p + 19 --- (1)
1 u + 30 = 4 p
1 u = 4 p - 30 --- (2)
(2) = (1)
4 p - 30 = 3 p + 19
4 p - 3 p = 19 + 30
1 p = 49
Total number of lollipops and candy canes
= (3 p + 19) + 4 p
= 7 p + 19
= 7 x 49 + 19
= 343 + 19
= 362
Answer(s): 362
