Opal packed some candy sticks for a party. She packed
23 of the candy sticks into 4 blue bags and the rest into 22 violet bags. There were 104 candy sticks altogether in 1 blue and 2 violet bags. How many candy sticks did Opal have at first?
| |
Blue bags |
Violet bags |
| Number of bags |
4 |
22 |
| Number of candy sticks |
2 u |
1 u |
Let 1 B be 1 blue bag.
Let 1 V be 1 violet bag.
2 u = 4 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 = 104 --- (3)
Substitute 1 B = 11 V into (3).
11 V + 2 V = 104
13 V = 104
1 V = 104 ÷ 13 = 8
From (2)
1 u = 22 V
1 u = 22 x 8 = 176
Number of candy sticks that Opal had at first
= 2 u + 1 u
= 3 u
= 3 x 176
= 528
Answer(s): 528
