Joelle packed some candies for a party. She packed
23 of the candies into 10 blue bags and the rest into 20 violet bags. There were 18 candies altogether in 1 blue and 2 violet bags. How many candies did Joelle have at first?
| |
Blue bags |
Violet bags |
| Number of bags |
10 |
20 |
| Number of candies |
2 u |
1 u |
Let 1 B be 1 blue bag.
Let 1 V be 1 violet bag.
2 u = 10 B
1 u = 5 B --- (1)
1 u = 20 V --- (2)
(1) = (2)
5 B = 20 V
1 B = 20 ÷ 5 = 4 V
1 B + 2 V = 18 --- (3)
Substitute 1 B = 4 V into (3).
4 V + 2 V = 18
6 V = 18
1 V = 18 ÷ 6 = 3
From (2)
1 u = 20 V
1 u = 20 x 3 = 60
Number of candies that Joelle had at first
= 2 u + 1 u
= 3 u
= 3 x 60
= 180
Answer(s): 180
