Cindy packed some lollipops for a party. She packed
45 of the lollipops into 8 blue bags and the rest into 24 violet bags. There were 160 lollipops altogether in 1 blue and 4 violet bags. How many lollipops did Cindy have at first?
| |
Blue bags |
Violet bags |
| Number of bags |
8 |
24 |
| Number of lollipops |
4 u |
1 u |
Let 1 B be 1 blue bag.
Let 1 V be 1 violet bag.
4 u = 8 B
1 u = 2 B --- (1)
1 u = 24 V --- (2)
(1) = (2)
2 B = 24 V
1 B = 24 ÷ 2 = 12 V
1 B + 4 V = 160 --- (3)
Substitute 1 B = 12 V into (3).
12 V + 4 V = 160
16 V = 160
1 V = 160 ÷ 16 = 10
From (2)
1 u = 24 V
1 u = 24 x 10 = 240
Number of lollipops that Cindy had at first
= 4 u + 1 u
= 5 u
= 5 x 240
= 1200
Answer(s): 1200
