Question 190365
# 3 

Q: <font color=red>Bob wants to have concrete driveway in front of his house. The driveway will measure 58 2/3 feet long and 18 1/2 feet wide; and will be 3/4 foot thick. How many cubic yards of cement will be needed for the driveway? Round your answer to the nearest cubic yard.  [1 cubic yd = 27 cubic feet]</font>



A: 


First, we need to convert all of the mixed fractions to improper fractions.


So let's convert {{{58&2/3}}} into an improper fraction



{{{58&2/3}}} Start with the first fraction



{{{58+2/3}}} Break up the mixed fraction into a sum of the whole part and the fraction part.



{{{58(3/3)+2/3}}} Multiply 58 by {{{3/3}}} (to get equal denominators)



{{{174/3+2/3}}} Multiply



{{{(174+2)/3}}} Add the fractions


 
{{{176/3}}} Combine like terms.



So {{{58&2/3=176/3}}}


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Now let's convert {{{18&1/2}}} into an improper fraction


{{{18&1/2}}} Start with the second fraction



{{{18+1/2}}} Break up the mixed fraction into a sum of the whole part and the fraction part.



{{{18(2/2)+1/2}}} Multiply 18 by {{{2/2}}} (to get equal denominators)



{{{36/2+1/2}}} Multiply



{{{(36+1)/2}}} Add the fractions



{{{37/2}}} Add



So {{{18&1/2=37/2}}}



So the length and width as improper fractions are {{{176/3}}} and {{{37/2}}}. In other words, {{{L=176/3}}} and {{{W=37/2}}}



Now remember, the volume of a rectangular block is 



{{{V=LWH}}} where L is the length, W is the width, and H is the height



{{{V=(176/3)(37/2)(3/4)}}} Plug in {{{L=176/3}}}, {{{W=37/2}}} and {{{H=3/4}}}



{{{V=(176*37*3)/(3*2*4)}}} Combine the fractions (note: just multiply the corresponding numerators and denominators)



{{{V=(22*2*4*37*3)/(3*2*4)}}} Factor {{{176}}} into {{{176=88*2=22*2*4}}}



{{{V=(22*cross(2)*cross(4)*37*cross(3))/(cross(3)*cross(2)*cross(4))}}} Cancel out the common terms.



{{{V=22*37}}} Simplify



{{{V=814}}} Multiply


So the volume of the concrete driveway is 814 cubic feet.


Now since we're given the equation


1 cubic yard = 27 cubic feet



we can multiply the figure 814 cubic feet by the fraction *[Tex \LARGE \frac{1 \ \mbox{cubic yard}}{27 \ \mbox{cubic feet}}]


So...


*[Tex \LARGE \left(814 \ \mbox{cubic feet}\right)\left(\frac{1 \ \mbox{cubic yard}}{27 \ \mbox{cubic feet}}\right) = \frac{814 \ \mbox{cubic yards}}{27 } \approx 30.148 \ \mbox{cubic yards}]



Now round to the nearest whole number to get 30 cubic yards



So Bob will need 30 cubic yards of cement to build the driveway.