Betty packed some candy sticks for a party. She packed
45 of the candy sticks into 24 blue bags and the rest into 18 violet bags. There were 12 candy sticks altogether in 1 blue and 3 violet bags. How many candy sticks did Betty have at first?
| |
Blue bags |
Violet bags |
| Number of bags |
24 |
18 |
| Number of candy sticks |
4 u |
1 u |
Let 1 B be 1 blue bag.
Let 1 V be 1 violet bag.
4 u = 24 B
1 u = 6 B --- (1)
1 u = 18 V --- (2)
(1) = (2)
6 B = 18 V
1 B = 18 ÷ 6 = 3 V
1 B + 3 V = 12 --- (3)
Substitute 1 B = 3 V into (3).
3 V + 3 V = 12
6 V = 12
1 V = 12 ÷ 6 = 2
From (2)
1 u = 18 V
1 u = 18 x 2 = 36
Number of candy sticks that Betty had at first
= 4 u + 1 u
= 5 u
= 5 x 36
= 180
Answer(s): 180
