Pamela has some chocolate bars and lollipops. If she packs a chocolate bar and a lollipop in each bag, there will be 10 lollipops left. If she packs 2 chocolate bars and 3 lollipops in each bag, there will be 22 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 + 10 |
2 p + 22 |
3 p |
| Change |
- 1 u |
- 1 u |
- 2 p |
- 3 p |
| After |
0 |
10 |
22 |
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 = 2 p + 22 --- (1)
1 u + 10 = 3 p
1 u = 3 p - 10 --- (2)
(2) = (1)
3 p - 10 = 2 p + 22
3 p - 2 p = 22 + 10
1 p = 32
Total number of chocolate bars and lollipops
= (2 p + 22) + 3 p
= 5 p + 22
= 5 x 32 + 22
= 160 + 22
= 182
Answer(s): 182
