Eva 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 2 candy canes and 3 mochi balls in each bag, there will be 22 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 |
2 p + 22 |
3 p |
| Change |
- 1 u |
- 1 u |
- 2 p |
- 3 p |
| After |
0 |
23 |
22 |
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 = 2 p + 22 --- (1)
1 u + 23 = 3 p
1 u = 3 p - 23 --- (2)
(2) = (1)
3 p - 23 = 2 p + 22
3 p - 2 p = 22 + 23
1 p = 45
Total number of candy canes and mochi balls
= (2 p + 22) + 3 p
= 5 p + 22
= 5 x 45 + 22
= 225 + 22
= 247
Answer(s): 247
