Cody had three boxes, containing a total of 980 styrofoam plates. The number of styrofoam plates in Box A to the total number of styrofoam plates was 3 : 7. He sold 400 styrofoam plates from Box B and sold
14 of the styrofoam plates in Box C. The number of styrofoam plates left in Box B to the number of styrofoam plates left in Box C was 2 : 1. How many styrofoam plates were there in Box B at first?
|
Box A |
Box B |
Box C |
Total |
Before |
3 u
|
4 u (560)
|
7 u (980) |
|
|
6 p + 400 |
4 p |
|
Change |
|
- 400 |
- 1 p |
|
|
|
|
3 p |
|
After |
|
2x3 = 6 p |
1x3 = 3 p |
|
7 u = 980
1 u = 980 ÷ 7 = 140
Number of styrofoam plates in Box B and Box C at first
= 4 u
= 4 x 140
= 560
The number of plates left in C is the repeated identity.
LCM of 1 and 3 = 3
6 p + 400 + 4 p = 560
6 p + 4 p = 560 - 400
10 p = 160
1 p = 160 ÷ 10 = 16
Number of plates in Box B at first
= 6 p + 400
= 6 x 16 + 400
= 96 + 400
= 496
Answer(s):496