Wendy has some chocolate bars and mochi balls. If she packs a chocolate bar and a mochi ball in each bag, there will be 19 mochi balls left. If she packs 3 chocolate bars and 4 mochi balls in each bag, there will be 22 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 + 19 |
3 p + 22 |
4 p |
Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
After |
0 |
19 |
22 |
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 = 3 p + 22 --- (1)
1 u + 19 = 4 p
1 u = 4 p - 19 --- (2)
(2) = (1)
4 p - 19 = 3 p + 22
4 p - 3 p = 22 + 19
1 p = 41
Total number of chocolate bars and mochi balls
= (3 p + 22) + 4 p
= 7 p + 22
= 7 x 41 + 22
= 287 + 22
= 309
Answer(s): 309