Betty has some candy canes and mochi balls. If she packs a candy cane and a mochi ball in each bag, there will be 10 mochi balls left. If she packs 5 candy canes and 6 mochi balls in each bag, there will be 17 candy canes left. How many candy canes and mochi balls does she have in all?
| |
Case 1 |
Case 2 |
| |
Candy Canes |
Mochi Balls |
Candy Canes |
Mochi Balls |
| Before |
1 u |
1 u + 10 |
5 p + 17 |
6 p |
| Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
| After |
0 |
10 |
17 |
0 |
The number of candy canes at first is the same for Case 1 and 2.
The number of mochi balls at first is also the same for Case 1 and 2.
1 u = 5 p + 17 --- (1)
1 u + 10 = 6 p
1 u = 6 p - 10 --- (2)
(2) = (1)
6 p - 10 = 5 p + 17
6 p - 5 p = 17 + 10
1 p = 27
Total number of candy canes and mochi balls
= (5 p + 17) + 6 p
= 11 p + 17
= 11 x 27 + 17
= 297 + 17
= 314
Answer(s): 314
