Irene has some caramel apples and lollipops. If she packs a caramel apple and a lollipop in each bag, there will be 23 lollipops left. If she packs 5 caramel apples and 6 lollipops in each bag, there will be 20 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 + 23 |
5 p + 20 |
6 p |
| Change |
- 1 u |
- 1 u |
- 5 p |
- 6 p |
| After |
0 |
23 |
20 |
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 = 5 p + 20 --- (1)
1 u + 23 = 6 p
1 u = 6 p - 23 --- (2)
(2) = (1)
6 p - 23 = 5 p + 20
6 p - 5 p = 20 + 23
1 p = 43
Total number of caramel apples and lollipops
= (5 p + 20) + 6 p
= 11 p + 20
= 11 x 43 + 20
= 473 + 20
= 493
Answer(s): 493
