Penelope has some mochi balls and sweets. If she packs a mochi ball and a sweet in each bag, there will be 26 sweets left. If she packs 2 mochi balls and 3 sweets in each bag, there will be 12 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 + 26 |
2 p + 12 |
3 p |
| Change |
- 1 u |
- 1 u |
- 2 p |
- 3 p |
| After |
0 |
26 |
12 |
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 = 2 p + 12 --- (1)
1 u + 26 = 3 p
1 u = 3 p - 26 --- (2)
(2) = (1)
3 p - 26 = 2 p + 12
3 p - 2 p = 12 + 26
1 p = 38
Total number of mochi balls and sweets
= (2 p + 12) + 3 p
= 5 p + 12
= 5 x 38 + 12
= 190 + 12
= 202
Answer(s): 202
