Dana packed some sweets for a party. She packed
56 of the sweets into 20 blue bags and the rest into 8 violet bags. There were 60 sweets altogether in 1 blue and 4 violet bags. How many sweets did Dana have at first?
| |
Blue bags |
Violet bags |
| Number of bags |
20 |
8 |
| Number of sweets |
5 u |
1 u |
Let 1 B be 1 blue bag.
Let 1 V be 1 violet bag.
5 u = 20 B
1 u = 4 B --- (1)
1 u = 8 V --- (2)
(1) = (2)
4 B = 8 V
1 B = 8 ÷ 4 = 2 V
1 B + 4 V = 60 --- (3)
Substitute 1 B = 2 V into (3).
2 V + 4 V = 60
6 V = 60
1 V = 60 ÷ 6 = 10
From (2)
1 u = 8 V
1 u = 8 x 10 = 80
Number of sweets that Dana had at first
= 5 u + 1 u
= 6 u
= 6 x 80
= 480
Answer(s): 480
