Irene packed some candies for a party. She packed
34 of the candies into 24 blue bags and the rest into 16 violet bags. There were 15 candies altogether in 1 blue and 3 violet bags. How many candies did Irene have at first?
| |
Blue bags |
Violet bags |
| Number of bags |
24 |
16 |
| Number of candies |
3 u |
1 u |
Let 1 B be 1 blue bag.
Let 1 V be 1 violet bag.
3 u = 24 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 + 3 V = 15 --- (3)
Substitute 1 B = 2 V into (3).
2 V + 3 V = 15
5 V = 15
1 V = 15 ÷ 5 = 3
From (2)
1 u = 16 V
1 u = 16 x 3 = 48
Number of candies that Irene had at first
= 3 u + 1 u
= 4 u
= 4 x 48
= 192
Answer(s): 192
