Penelope has some sweets and lollipops. If she packs a sweet and a lollipop in each bag, there will be 25 lollipops left. If she packs 3 sweets and 4 lollipops in each bag, there will be 12 sweets left. How many sweets and lollipops does she have in all?
| |
Case 1 |
Case 2 |
| |
Sweets |
Lollipops |
Sweets |
Lollipops |
| Before |
1 u |
1 u + 25 |
3 p + 12 |
4 p |
| Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
| After |
0 |
25 |
12 |
0 |
The number of sweets 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 = 3 p + 12 --- (1)
1 u + 25 = 4 p
1 u = 4 p - 25 --- (2)
(2) = (1)
4 p - 25 = 3 p + 12
4 p - 3 p = 12 + 25
1 p = 37
Total number of sweets and lollipops
= (3 p + 12) + 4 p
= 7 p + 12
= 7 x 37 + 12
= 259 + 12
= 271
Answer(s): 271
