Brandon had three boxes, containing a total of 1040 styrofoam bowls. The number of styrofoam bowls in Box P to the total number of styrofoam bowls was 3 : 8. He sold 480 styrofoam bowls from Box Q and sold
15 of the styrofoam bowls in Box R. The number of styrofoam bowls left in Box Q to the number of styrofoam bowls left in Box R was 3 : 1. How many styrofoam bowls were there in Box Q at first?
|
Box P |
Box Q |
Box R |
Total |
Before |
3 u
|
5 u (650)
|
8 u (1040) |
|
|
12 p + 480 |
5 p |
|
Change |
|
- 480 |
- 1 p |
|
|
|
|
4 p |
|
After |
|
3x4 = 12 p |
1x4 = 4 p |
|
8 u = 1040
1 u = 1040 ÷ 8 = 130
Number of styrofoam bowls in Box Q and Box R at first
= 5 u
= 5 x 130
= 650
The number of bowls left in R is the repeated identity.
LCM of 1 and 4 = 4
12 p + 480 + 5 p = 650
12 p + 5 p = 650 - 480
17 p = 170
1 p = 170 ÷ 17 = 10
Number of bowls in Box Q at first
= 12 p + 480
= 12 x 10 + 480
= 120 + 480
= 600
Answer(s):600