Olivia has some candy canes and mochi balls. If she packs a candy cane and a mochi ball in each bag, there will be 24 mochi balls left. If she packs 3 candy canes and 4 mochi balls in each bag, there will be 29 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 + 24 |
3 p + 29 |
4 p |
Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
After |
0 |
24 |
29 |
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 = 3 p + 29 --- (1)
1 u + 24 = 4 p
1 u = 4 p - 24 --- (2)
(2) = (1)
4 p - 24 = 3 p + 29
4 p - 3 p = 29 + 24
1 p = 53
Total number of candy canes and mochi balls
= (3 p + 29) + 4 p
= 7 p + 29
= 7 x 53 + 29
= 371 + 29
= 400
Answer(s): 400