Gabby has some mochi balls and sweets. If she packs a mochi ball and a sweet in each bag, there will be 10 sweets left. If she packs 5 mochi balls and 6 sweets in each bag, there will be 18 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 + 10 |
5 p + 18 |
6 p |
| Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
| After |
0 |
10 |
18 |
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 = 5 p + 18 --- (1)
1 u + 10 = 6 p
1 u = 6 p - 10 --- (2)
(2) = (1)
6 p - 10 = 5 p + 18
6 p - 5 p = 18 + 10
1 p = 28
Total number of mochi balls and sweets
= (5 p + 18) + 6 p
= 11 p + 18
= 11 x 28 + 18
= 308 + 18
= 326
Answer(s): 326
