Risa has some sweets and chocolate bars. If she packs a sweet and a chocolate bar in each bag, there will be 28 chocolate bars left. If she packs 4 sweets and 5 chocolate bars in each bag, there will be 14 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 + 28 |
4 p + 14 |
5 p |
| Change |
- 1 u |
- 1 u |
- 4 p |
- 5 p |
| After |
0 |
28 |
14 |
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 = 4 p + 14 --- (1)
1 u + 28 = 5 p
1 u = 5 p - 28 --- (2)
(2) = (1)
5 p - 28 = 4 p + 14
5 p - 4 p = 14 + 28
1 p = 42
Total number of sweets and chocolate bars
= (4 p + 14) + 5 p
= 9 p + 14
= 9 x 42 + 14
= 378 + 14
= 392
Answer(s): 392
