Emma has some sweets and chocolate bars. If she packs a sweet and a chocolate bar in each bag, there will be 27 chocolate bars left. If she packs 3 sweets and 4 chocolate bars in each bag, there will be 25 sweets left. How many sweets and chocolate bars does she have in all?
| |
Case 1 |
Case 2 |
| |
Sweets |
Chocolate Bars |
Sweets |
Chocolate Bars |
| Before |
1 u |
1 u + 27 |
3 p + 25 |
4 p |
| Change |
- 1 u |
- 1 u |
- 3 p |
- 4 p |
| After |
0 |
27 |
25 |
0 |
The number of sweets at first is the same for Case 1 and 2.
The number of chocolate bars at first is also the same for Case 1 and 2.
1 u = 3 p + 25 --- (1)
1 u + 27 = 4 p
1 u = 4 p - 27 --- (2)
(2) = (1)
4 p - 27 = 3 p + 25
4 p - 3 p = 25 + 27
1 p = 52
Total number of sweets and chocolate bars
= (3 p + 25) + 4 p
= 7 p + 25
= 7 x 52 + 25
= 364 + 25
= 389
Answer(s): 389
