QuestionA customer wants $61 / 4^{\prime \prime}$ pieces of $1 / 2$ ' roundstock from a $48^{\prime \prime}$ piece. How many can you provide, considering $1 / 8^{\text{"}}$ waste?

Studdy Solution

STEP 1

Assumptions1. The length of the roundstock on hand is $48''$ . The length of each piece required by the customer is $61 /4''$
3. There is a kerf waste of $1 /8''$ for each cut

STEP 2

First, we need to convert the length of each piece required by the customer from fractional inches to decimal inches. $Length\, of\, each\, piece =61 /4 =15.25''$

STEP 3

Next, we need to account for the kerf waste for each cut. Since each cut results in a waste of $1 /8''$ , the total length of each piece including the waste is the sum of the length of each piece and the kerf waste.
$Total\, length\, of\, each\, piece = Length\, of\, each\, piece + Kerf\, waste$

STEP 4

Plug in the values for the length of each piece and the kerf waste to calculate the total length of each piece.
$Total\, length\, of\, each\, piece =15.25'' +1 /8''$

STEP 5

Convert the kerf waste from fractional inches to decimal inches.
$1 /8'' =0.125''$ $Total\, length\, of\, each\, piece =15.25'' +0.125''$

STEP 6

Calculate the total length of each piece.
$Total\, length\, of\, each\, piece =15.25'' +0.125'' =15.375''$

STEP 7

Now that we have the total length of each piece, we can find out how many such pieces we can get from the $48''$ roundstock. This can be done by dividing the length of the roundstock by the total length of each piece.
$Number\, of\, pieces = Length\, of\, roundstock / Total\, length\, of\, each\, piece$

STEP 8

Plug in the values for the length of the roundstock and the total length of each piece to calculate the number of pieces.
$Number\, of\, pieces =48'' /15.375''$

STEP 9

Calculate the number of pieces. Since we cannot deliver a fraction of a piece, we take the floor of the result.
$Number\, of\, pieces = \lfloor48'' /15.375'' \rfloor =3$ You can deliver3 pieces of $61 /4''$ roundstock.

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QuestionA customer wants $61 / 4^{\prime \prime}$ pieces of $1 / 2$ ' roundstock from a $48^{\prime \prime}$ piece. How many can you provide, considering $1 / 8^{\text{"}}$ waste?

Studdy Solution

STEP 1

Assumptions1. The length of the roundstock on hand is $48''$ . The length of each piece required by the customer is $61 /4''$
3. There is a kerf waste of $1 /8''$ for each cut

STEP 2

First, we need to convert the length of each piece required by the customer from fractional inches to decimal inches. $Length\, of\, each\, piece =61 /4 =15.25''$

STEP 3

Next, we need to account for the kerf waste for each cut. Since each cut results in a waste of $1 /8''$ , the total length of each piece including the waste is the sum of the length of each piece and the kerf waste.
$Total\, length\, of\, each\, piece = Length\, of\, each\, piece + Kerf\, waste$

STEP 4

Plug in the values for the length of each piece and the kerf waste to calculate the total length of each piece.
$Total\, length\, of\, each\, piece =15.25'' +1 /8''$

STEP 5

Convert the kerf waste from fractional inches to decimal inches.
$1 /8'' =0.125''$ $Total\, length\, of\, each\, piece =15.25'' +0.125''$

STEP 6

Calculate the total length of each piece.
$Total\, length\, of\, each\, piece =15.25'' +0.125'' =15.375''$

STEP 7

STEP 8

Plug in the values for the length of the roundstock and the total length of each piece to calculate the number of pieces.
$Number\, of\, pieces =48'' /15.375''$

STEP 9

Calculate the number of pieces. Since we cannot deliver a fraction of a piece, we take the floor of the result.
$Number\, of\, pieces = \lfloor48'' /15.375'' \rfloor =3$ You can deliver3 pieces of $61 /4''$ roundstock.

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QuestionA customer wants 61/4′′61 / 4^{\prime \prime}61/4′′ pieces of 1/21 / 21/2' roundstock from a 48′′48^{\prime \prime}48′′ piece. How many can you provide, considering 1/8"1 / 8^{\text{"}}1/8" waste?

Studdy Solution

STEP 1

Assumptions1. The length of the roundstock on hand is 48′′48''48′′ . The length of each piece required by the customer is 61/4′′61 /4''61/4′′3. There is a kerf waste of 1/8′′1 /8''1/8′′ for each cut

STEP 2

First, we need to convert the length of each piece required by the customer from fractional inches to decimal inches.Length of each piece=61/4=15.25′′Length\, of\, each\, piece =61 /4 =15.25''Lengthofeachpiece=61/4=15.25′′

STEP 3

STEP 4

Plug in the values for the length of each piece and the kerf waste to calculate the total length of each piece.Total length of each piece=15.25′′+1/8′′Total\, length\, of\, each\, piece =15.25'' +1 /8''Totallengthofeachpiece=15.25′′+1/8′′

STEP 5

Convert the kerf waste from fractional inches to decimal inches.1/8′′=0.125′′1 /8'' =0.125''1/8′′=0.125′′Total length of each piece=15.25′′+0.125′′Total\, length\, of\, each\, piece =15.25'' +0.125''Totallengthofeachpiece=15.25′′+0.125′′

STEP 6

Calculate the total length of each piece.Total length of each piece=15.25′′+0.125′′=15.375′′Total\, length\, of\, each\, piece =15.25'' +0.125'' =15.375''Totallengthofeachpiece=15.25′′+0.125′′=15.375′′

STEP 7

STEP 8

Plug in the values for the length of the roundstock and the total length of each piece to calculate the number of pieces.Number of pieces=48′′/15.375′′Number\, of\, pieces =48'' /15.375''Numberofpieces=48′′/15.375′′

STEP 9

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QuestionA customer wants $61 / 4^{\prime \prime}$ pieces of $1 / 2$ ' roundstock from a $48^{\prime \prime}$ piece. How many can you provide, considering $1 / 8^{\text{"}}$ waste?

Assumptions1. The length of the roundstock on hand is $48''$ . The length of each piece required by the customer is $61 /4''$
3. There is a kerf waste of $1 /8''$ for each cut

First, we need to convert the length of each piece required by the customer from fractional inches to decimal inches. $Length\, of\, each\, piece =61 /4 =15.25''$

Plug in the values for the length of each piece and the kerf waste to calculate the total length of each piece.
$Total\, length\, of\, each\, piece =15.25'' +1 /8''$

Convert the kerf waste from fractional inches to decimal inches.
$1 /8'' =0.125''$ $Total\, length\, of\, each\, piece =15.25'' +0.125''$

Calculate the total length of each piece.
$Total\, length\, of\, each\, piece =15.25'' +0.125'' =15.375''$

Plug in the values for the length of the roundstock and the total length of each piece to calculate the number of pieces.
$Number\, of\, pieces =48'' /15.375''$