Dana packed some candies for a party. She packed
56 of the candies into 40 blue bags and the rest into 16 violet bags. There were 12 candies altogether in 1 blue and 4 violet bags. How many candies did Dana have at first?
| |
Blue bags |
Violet bags |
| Number of bags |
40 |
16 |
| Number of candies |
5 u |
1 u |
Let 1 B be 1 blue bag.
Let 1 V be 1 violet bag.
5 u = 40 B
1 u = 8 B --- (1)
1 u = 16 V --- (2)
(1) = (2)
8 B = 16 V
1 B = 16 ÷ 8 = 2 V
1 B + 4 V = 12 --- (3)
Substitute 1 B = 2 V into (3).
2 V + 4 V = 12
6 V = 12
1 V = 12 ÷ 6 = 2
From (2)
1 u = 16 V
1 u = 16 x 2 = 32
Number of candies that Dana had at first
= 5 u + 1 u
= 6 u
= 6 x 32
= 192
Answer(s): 192
