Opal packed some sweets for a party. She packed
67 of the sweets into 30 blue bags and the rest into 15 violet bags. There were 28 sweets altogether in 1 blue and 4 violet bags. How many sweets did Opal have at first?
| |
Blue bags |
Violet bags |
| Number of bags |
30 |
15 |
| Number of sweets |
6 u |
1 u |
Let 1 B be 1 blue bag.
Let 1 V be 1 violet bag.
6 u = 30 B
1 u = 5 B --- (1)
1 u = 15 V --- (2)
(1) = (2)
5 B = 15 V
1 B = 15 ÷ 5 = 3 V
1 B + 4 V = 28 --- (3)
Substitute 1 B = 3 V into (3).
3 V + 4 V = 28
7 V = 28
1 V = 28 ÷ 7 = 4
From (2)
1 u = 15 V
1 u = 15 x 4 = 60
Number of sweets that Opal had at first
= 6 u + 1 u
= 7 u
= 7 x 60
= 420
Answer(s): 420
