Jane has some chocolate bars and mochi balls. If she packs a chocolate bar and a mochi ball in each bag, there will be 22 mochi balls left. If she packs 2 chocolate bars and 3 mochi balls in each bag, there will be 30 chocolate bars left. How many chocolate bars and mochi balls does she have in all?
|
Case 1 |
Case 2 |
|
Chocolate Bars |
Mochi Balls |
Chocolate Bars |
Mochi Balls |
Before |
1 u |
1 u + 22 |
2 p + 30 |
3 p |
Change |
- 1 u |
- 1 u |
- 2 p |
- 3 p |
After |
0 |
22 |
30 |
0 |
The number of chocolate bars 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 + 30 --- (1)
1 u + 22 = 3 p
1 u = 3 p - 22 --- (2)
(2) = (1)
3 p - 22 = 2 p + 30
3 p - 2 p = 30 + 22
1 p = 52
Total number of chocolate bars and mochi balls
= (2 p + 30) + 3 p
= 5 p + 30
= 5 x 52 + 30
= 260 + 30
= 290
Answer(s): 290