Tiffany has some sweets and mochi balls. If she packs a sweet and a mochi ball in each bag, there will be 27 mochi balls left. If she packs 5 sweets and 6 mochi balls in each bag, there will be 20 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 + 27 |
5 p + 20 |
6 p |
| Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
| After |
0 |
27 |
20 |
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 + 20 --- (1)
1 u + 27 = 6 p
1 u = 6 p - 27 --- (2)
(2) = (1)
6 p - 27 = 5 p + 20
6 p - 5 p = 20 + 27
1 p = 47
Total number of sweets and mochi balls
= (5 p + 20) + 6 p
= 11 p + 20
= 11 x 47 + 20
= 517 + 20
= 537
Answer(s): 537
