Min has some candy canes and mochi balls. If she packs a candy cane and a mochi ball in each bag, there will be 23 mochi balls left. If she packs 4 candy canes and 5 mochi balls in each bag, there will be 15 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 + 23 |
4 p + 15 |
5 p |
| Change |
- 1 u |
- 1 u |
- 4 p |
- 5 p |
| After |
0 |
23 |
15 |
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 = 4 p + 15 --- (1)
1 u + 23 = 5 p
1 u = 5 p - 23 --- (2)
(2) = (1)
5 p - 23 = 4 p + 15
5 p - 4 p = 15 + 23
1 p = 38
Total number of candy canes and mochi balls
= (4 p + 15) + 5 p
= 9 p + 15
= 9 x 38 + 15
= 342 + 15
= 357
Answer(s): 357
