Kylie has some candy canes and sweets. If she packs a candy cane and a sweet in each bag, there will be 21 sweets left. If she packs 3 candy canes and 4 sweets in each bag, there will be 23 candy canes left. How many candy canes and sweets does she have in all?
| |
Case 1 |
Case 2 |
| |
Candy Canes |
Sweets |
Candy Canes |
Sweets |
| Before |
1 u |
1 u + 21 |
3 p + 23 |
4 p |
| Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
| After |
0 |
21 |
23 |
0 |
The number of candy canes at first is the same for Case 1 and 2.
The number of sweets at first is also the same for Case 1 and 2.
1 u = 3 p + 23 --- (1)
1 u + 21 = 4 p
1 u = 4 p - 21 --- (2)
(2) = (1)
4 p - 21 = 3 p + 23
4 p - 3 p = 23 + 21
1 p = 44
Total number of candy canes and sweets
= (3 p + 23) + 4 p
= 7 p + 23
= 7 x 44 + 23
= 308 + 23
= 331
Answer(s): 331
