Penelope has some lollipops and mochi balls. If she packs a lollipop and a mochi ball in each bag, there will be 28 mochi balls left. If she packs 5 lollipops and 6 mochi balls in each bag, there will be 27 lollipops left. How many lollipops and mochi balls does she have in all?
| |
Case 1 |
Case 2 |
| |
Lollipops |
Mochi Balls |
Lollipops |
Mochi Balls |
| Before |
1 u |
1 u + 28 |
5 p + 27 |
6 p |
| Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
| After |
0 |
28 |
27 |
0 |
The number of lollipops 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 + 27 --- (1)
1 u + 28 = 6 p
1 u = 6 p - 28 --- (2)
(2) = (1)
6 p - 28 = 5 p + 27
6 p - 5 p = 27 + 28
1 p = 55
Total number of lollipops and mochi balls
= (5 p + 27) + 6 p
= 11 p + 27
= 11 x 55 + 27
= 605 + 27
= 632
Answer(s): 632
