Wendy packed some chocolate bars for a party. She packed
23 of the chocolate bars into 14 blue bags and the rest into 14 violet bags. There were 45 chocolate bars altogether in 1 blue and 3 violet bags. How many chocolate bars did Wendy have at first?
| |
Blue bags |
Violet bags |
| Number of bags |
14 |
14 |
| Number of chocolate bars |
2 u |
1 u |
Let 1 B be 1 blue bag.
Let 1 V be 1 violet bag.
2 u = 14 B
1 u = 7 B --- (1)
1 u = 14 V --- (2)
(1) = (2)
7 B = 14 V
1 B = 14 ÷ 7 = 2 V
1 B + 3 V = 45 --- (3)
Substitute 1 B = 2 V into (3).
2 V + 3 V = 45
5 V = 45
1 V = 45 ÷ 5 = 9
From (2)
1 u = 14 V
1 u = 14 x 9 = 126
Number of chocolate bars that Wendy had at first
= 2 u + 1 u
= 3 u
= 3 x 126
= 378
Answer(s): 378
