Olivia has some lollipops and chocolate bars. If she packs a lollipop and a chocolate bar in each bag, there will be 17 chocolate bars left. If she packs 5 lollipops and 6 chocolate bars in each bag, there will be 22 lollipops left. How many lollipops and chocolate bars does she have in all?
| |
Case 1 |
Case 2 |
| |
Lollipops |
Chocolate Bars |
Lollipops |
Chocolate Bars |
| Before |
1 u |
1 u + 17 |
5 p + 22 |
6 p |
| Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
| After |
0 |
17 |
22 |
0 |
The number of lollipops at first is the same for Case 1 and 2.
The number of chocolate bars at first is also the same for Case 1 and 2.
1 u = 5 p + 22 --- (1)
1 u + 17 = 6 p
1 u = 6 p - 17 --- (2)
(2) = (1)
6 p - 17 = 5 p + 22
6 p - 5 p = 22 + 17
1 p = 39
Total number of lollipops and chocolate bars
= (5 p + 22) + 6 p
= 11 p + 22
= 11 x 39 + 22
= 429 + 22
= 451
Answer(s): 451
