Barbara packed some lollipops for a party. She packed
56 of the lollipops into 20 blue bags and the rest into 16 violet bags. There were 56 lollipops altogether in 1 blue and 3 violet bags. How many lollipops did Barbara have at first?
|
Blue bags |
Violet bags |
Number of bags |
20 |
16 |
Number of lollipops |
5 u |
1 u |
Let 1 B be 1 blue bag.
Let 1 V be 1 violet bag.
5 u = 20 B
1 u = 4 B --- (1)
1 u = 16 V --- (2)
(1) = (2)
4 B = 16 V
1 B = 16 ÷ 4 = 4 V
1 B + 3 V = 56 --- (3)
Substitute 1 B = 4 V into (3).
4 V + 3 V = 56
7 V = 56
1 V = 56 ÷ 7 = 8
From (2)
1 u = 16 V
1 u = 16 x 8 = 128
Number of lollipops that Barbara had at first
= 5 u + 1 u
= 6 u
= 6 x 128
= 768
Answer(s): 768