Cindy has some chocolate bars and lollipops. If she packs a chocolate bar and a lollipop in each bag, there will be 18 lollipops left. If she packs 5 chocolate bars and 6 lollipops in each bag, there will be 13 chocolate bars left. How many chocolate bars and lollipops does she have in all?
| |
Case 1 |
Case 2 |
| |
Chocolate Bars |
Lollipops |
Chocolate Bars |
Lollipops |
| Before |
1 u |
1 u + 18 |
5 p + 13 |
6 p |
| Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
| After |
0 |
18 |
13 |
0 |
The number of chocolate bars at first is the same for Case 1 and 2.
The number of lollipops at first is also the same for Case 1 and 2.
1 u = 5 p + 13 --- (1)
1 u + 18 = 6 p
1 u = 6 p - 18 --- (2)
(2) = (1)
6 p - 18 = 5 p + 13
6 p - 5 p = 13 + 18
1 p = 31
Total number of chocolate bars and lollipops
= (5 p + 13) + 6 p
= 11 p + 13
= 11 x 31 + 13
= 341 + 13
= 354
Answer(s): 354
