Opal has some sweets and mochi balls. If she packs a sweet and a mochi ball in each bag, there will be 19 mochi balls left. If she packs 5 sweets and 6 mochi balls in each bag, there will be 29 sweets left. How many sweets and mochi balls does she have in all?
|
Case 1 |
Case 2 |
|
Sweets |
Mochi Balls |
Sweets |
Mochi Balls |
Before |
1 u |
1 u + 19 |
5 p + 29 |
6 p |
Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
After |
0 |
19 |
29 |
0 |
The number of sweets 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 = 5 p + 29 --- (1)
1 u + 19 = 6 p
1 u = 6 p - 19 --- (2)
(2) = (1)
6 p - 19 = 5 p + 29
6 p - 5 p = 29 + 19
1 p = 48
Total number of sweets and mochi balls
= (5 p + 29) + 6 p
= 11 p + 29
= 11 x 48 + 29
= 528 + 29
= 557
Answer(s): 557