Julie packed some candies for a party. She packed
34 of the candies into 12 blue bags and the rest into 8 violet bags. There were 10 candies altogether in 1 blue and 3 violet bags. How many candies did Julie have at first?
| |
Blue bags |
Violet bags |
| Number of bags |
12 |
8 |
| Number of candies |
3 u |
1 u |
Let 1 B be 1 blue bag.
Let 1 V be 1 violet bag.
3 u = 12 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 + 3 V = 10 --- (3)
Substitute 1 B = 2 V into (3).
2 V + 3 V = 10
5 V = 10
1 V = 10 ÷ 5 = 2
From (2)
1 u = 8 V
1 u = 8 x 2 = 16
Number of candies that Julie had at first
= 3 u + 1 u
= 4 u
= 4 x 16
= 64
Answer(s): 64
