Usha has some lollipops and caramel apples. If she packs a lollipop and a caramel apple in each bag, there will be 19 caramel apples left. If she packs 4 lollipops and 5 caramel apples in each bag, there will be 28 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 + 19 |
4 p + 28 |
5 p |
| Change |
- 1 u |
- 1 u |
- 4 p |
- 5 p |
| After |
0 |
19 |
28 |
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 = 4 p + 28 --- (1)
1 u + 19 = 5 p
1 u = 5 p - 19 --- (2)
(2) = (1)
5 p - 19 = 4 p + 28
5 p - 4 p = 28 + 19
1 p = 47
Total number of lollipops and caramel apples
= (4 p + 28) + 5 p
= 9 p + 28
= 9 x 47 + 28
= 423 + 28
= 451
Answer(s): 451
