Roshel has some lollipops and caramel apples. If she packs a lollipop and a caramel apple in each bag, there will be 28 caramel apples left. If she packs 3 lollipops and 4 caramel apples in each bag, there will be 30 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 + 28 |
3 p + 30 |
4 p |
| Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
| After |
0 |
28 |
30 |
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 = 3 p + 30 --- (1)
1 u + 28 = 4 p
1 u = 4 p - 28 --- (2)
(2) = (1)
4 p - 28 = 3 p + 30
4 p - 3 p = 30 + 28
1 p = 58
Total number of lollipops and caramel apples
= (3 p + 30) + 4 p
= 7 p + 30
= 7 x 58 + 30
= 406 + 30
= 436
Answer(s): 436
