Raeann has some mochi balls and sweets. If she packs a mochi ball and a sweet in each bag, there will be 12 sweets left. If she packs 4 mochi balls and 5 sweets in each bag, there will be 20 mochi balls left. How many mochi balls and sweets does she have in all?
| |
Case 1 |
Case 2 |
| |
Mochi Balls |
Sweets |
Mochi Balls |
Sweets |
| Before |
1 u |
1 u + 12 |
4 p + 20 |
5 p |
| Change |
- 1 u |
- 1 u |
- 4 p |
- 5 p |
| After |
0 |
12 |
20 |
0 |
The number of mochi balls at first is the same for Case 1 and 2.
The number of sweets at first is also the same for Case 1 and 2.
1 u = 4 p + 20 --- (1)
1 u + 12 = 5 p
1 u = 5 p - 12 --- (2)
(2) = (1)
5 p - 12 = 4 p + 20
5 p - 4 p = 20 + 12
1 p = 32
Total number of mochi balls and sweets
= (4 p + 20) + 5 p
= 9 p + 20
= 9 x 32 + 20
= 288 + 20
= 308
Answer(s): 308
