Emma has some lollipops and caramel apples. If she packs a lollipop and a caramel apple in each bag, there will be 12 caramel apples left. If she packs 2 lollipops and 3 caramel apples in each bag, there will be 25 lollipops left. How many lollipops and caramel apples does she have in all?
| |
Case 1 |
Case 2 |
| |
Lollipops |
Caramel Apples |
Lollipops |
Caramel Apples |
| Before |
1 u |
1 u + 12 |
2 p + 25 |
3 p |
| Change |
- 1 u |
- 1 u |
- 2 p |
- 3 p |
| After |
0 |
12 |
25 |
0 |
The number of lollipops at first is the same for Case 1 and 2.
The number of caramel apples at first is also the same for Case 1 and 2.
1 u = 2 p + 25 --- (1)
1 u + 12 = 3 p
1 u = 3 p - 12 --- (2)
(2) = (1)
3 p - 12 = 2 p + 25
3 p - 2 p = 25 + 12
1 p = 37
Total number of lollipops and caramel apples
= (2 p + 25) + 3 p
= 5 p + 25
= 5 x 37 + 25
= 185 + 25
= 210
Answer(s): 210
