A Certain type of board is sold only in length of multiples of 2 feet from 6 ft to 24 ft. A builder needs a large quantity of this type of board in 5 1/2 foot lengths for minimum waste. The lengths in feet to be ordered should be
(A) 6
(B) 12
(C) 16
(D) 18
(E) 22
(F) 24
not just answer
Think about multiples of 5.5.
What is your answer?
i mean E
E is right.
11, 16.5, 22
i still not understand
what is 2 feet from 6 ft to 24 ft.
The boards are sold in multiples of 2 feet. That is, the boards are sold in the following lengths:
6, 8, 10, 12, 14, 16, 18, 20, 22, and 24 feet.
i understand now, thank you
:-) You're welcome.
To find the lengths in feet that should be ordered, we need to consider the requirements given in the problem statement. The type of board being sold is only available in lengths of multiples of 2 feet from 6 ft to 24 ft. The builder needs boards in 5 1/2 foot lengths to minimize waste.
The first step is to convert the desired length of 5 1/2 feet into an equivalent fraction with a denominator of 2: 5 1/2 = 11/2.
Next, we need to determine which available board lengths will allow for minimal waste when cut into 5 1/2 foot pieces. We can do this by dividing each available board length by the desired length of 11/2 (5 1/2 feet).
Let's calculate:
6/ (11/2) = 12/11 = 1 remainder 1
12/ (11/2) = 24/11 = 2 remainder 2
16/ (11/2) = 32/11 = 2 remainder 10
18/ (11/2) = 36/11 = 3 remainder 3
22/ (11/2) = 44/11 = 4 remainder 0
24/ (11/2) = 48/11 = 4 remainder 4
Now, let's analyze the remainders. The remainder represents the amount of wasted board length when we divide the available board length by the desired length.
From the calculations above, we see that the remainders are:
- 1 for 6 ft
- 2 for 12 ft
- 10 for 16 ft
- 3 for 18 ft
- 0 for 22 ft
- 4 for 24 ft
To minimize waste, we would like the remainder to be as close to zero as possible. Therefore, the lengths in feet to be ordered should be those that have a remainder of zero.
From the options provided:
(A) 6 - remainder 1
(B) 12 - remainder 2
(C) 16 - remainder 10
(D) 18 - remainder 3
(E) 22 - remainder 0
(F) 24 - remainder 4
Only option (E) 22 has a remainder of zero, indicating that it will result in the least amount of waste when cut into 5 1/2 foot lengths.
Therefore, the lengths to be ordered should be 22 feet.