Esther packed some candies for a party. She packed
34 of the candies into 6 blue bags and the rest into 22 violet bags. There were 117 candies altogether in 1 blue and 2 violet bags. How many candies did Esther have at first?
| |
Blue bags |
Violet bags |
| Number of bags |
6 |
22 |
| Number of candies |
3 u |
1 u |
Let 1 B be 1 blue bag.
Let 1 V be 1 violet bag.
3 u = 6 B
1 u = 2 B --- (1)
1 u = 22 V --- (2)
(1) = (2)
2 B = 22 V
1 B = 22 ÷ 2 = 11 V
1 B + 2 V = 117 --- (3)
Substitute 1 B = 11 V into (3).
11 V + 2 V = 117
13 V = 117
1 V = 117 ÷ 13 = 9
From (2)
1 u = 22 V
1 u = 22 x 9 = 198
Number of candies that Esther had at first
= 3 u + 1 u
= 4 u
= 4 x 198
= 792
Answer(s): 792
