Math

QuestionHow many 61/461 / 4^{\prime \prime} pieces can you cut from a 48" roundstock? Ignore kerf waste.

Studdy Solution

STEP 1

Assumptions1. The length of the roundstock on hand is48" . The customer needs pieces of length 61/461 /4^{\prime \prime}
3. We disregard kerf waste (the material removed by the cut)

STEP 2

First, we need to convert the length of the pieces the customer needs from a mixed number to a decimal. This can be done by dividing the numerator by the denominator and adding the whole number.
Lengthofpieces=Wholenumber+umeratorDenominatorLength\, of\, pieces = Whole\, number + \frac{umerator}{Denominator}

STEP 3

Now, plug in the given values for the whole number, numerator, and denominator to calculate the length of the pieces.
Lengthofpieces=61+1Length\, of\, pieces =61 + \frac{1}{}

STEP 4

Calculate the length of the pieces.
Lengthofpieces=61+14=61.25Length\, of\, pieces =61 + \frac{1}{4} =61.25^{\prime \prime}

STEP 5

Now that we have the length of the pieces the customer needs, we can find out how many pieces can be cut from the roundstock on hand. This can be done by dividing the length of the roundstock by the length of the pieces.
Numberofpieces=LengthofroundstockLengthofpiecesNumber\, of\, pieces = \frac{Length\, of\, roundstock}{Length\, of\, pieces}

STEP 6

Plug in the values for the length of the roundstock and the length of the pieces to calculate the number of pieces.
Numberofpieces=4861.25Number\, of\, pieces = \frac{48^{\prime \prime}}{61.25^{\prime \prime}}

STEP 7

Calculate the number of pieces. Since we cannot deliver a fraction of a piece, we need to round down to the nearest whole number.
Numberofpieces=4861.25Number\, of\, pieces = \lfloor \frac{48^{\prime \prime}}{61.25^{\prime \prime}} \rfloor

STEP 8

Calculate the number of pieces.
Numberofpieces=4861.25=0Number\, of\, pieces = \lfloor \frac{48^{\prime \prime}}{61.25^{\prime \prime}} \rfloor =0You can deliver0 pieces of 61/461 /4^{\prime \prime} from a48" piece of roundstock.

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