Usha has some caramel apples and lollipops. If she packs a caramel apple and a lollipop in each bag, there will be 22 lollipops left. If she packs 2 caramel apples and 3 lollipops in each bag, there will be 11 caramel apples left. How many caramel apples and lollipops does she have in all?
| |
Case 1 |
Case 2 |
| |
Caramel Apples |
Lollipops |
Caramel Apples |
Lollipops |
| Before |
1 u |
1 u + 22 |
2 p + 11 |
3 p |
| Change |
- 1 u |
- 1 u |
- 2 p |
- 3 p |
| After |
0 |
22 |
11 |
0 |
The number of caramel apples 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 + 11 --- (1)
1 u + 22 = 3 p
1 u = 3 p - 22 --- (2)
(2) = (1)
3 p - 22 = 2 p + 11
3 p - 2 p = 11 + 22
1 p = 33
Total number of caramel apples and lollipops
= (2 p + 11) + 3 p
= 5 p + 11
= 5 x 33 + 11
= 165 + 11
= 176
Answer(s): 176
