Jack had three boxes, containing a total of 1120 styrofoam plates. The number of styrofoam plates in Box A to the total number of styrofoam plates was 3 : 8. He sold 377 styrofoam plates from Box B and sold
15 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 3 : 1. How many styrofoam plates were there in Box B at first?
|
Box A |
Box B |
Box C |
Total |
Before |
3 u
|
5 u (700)
|
8 u (1120) |
|
|
12 p + 377 |
5 p |
|
Change |
|
- 377 |
- 1 p |
|
|
|
|
4 p |
|
After |
|
3x4 = 12 p |
1x4 = 4 p |
|
8 u = 1120
1 u = 1120 ÷ 8 = 140
Number of styrofoam plates in Box B and Box C at first
= 5 u
= 5 x 140
= 700
The number of plates left in C is the repeated identity.
LCM of 1 and 4 = 4
12 p + 377 + 5 p = 700
12 p + 5 p = 700 - 377
17 p = 323
1 p = 323 ÷ 17 = 19
Number of plates in Box B at first
= 12 p + 377
= 12 x 19 + 377
= 228 + 377
= 605
Answer(s):605