SOLUTION: # 3. 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

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: # 3. 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       Log On


   

Question 190365: # 3. 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]





Answer by jim_thompson5910(35256) About Me  (Show Source):
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# 3
Q: 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]


A:

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

So let's convert 58%262%2F3 into an improper fraction


58%262%2F3 Start with the first fraction


58%2B2%2F3 Break up the mixed fraction into a sum of the whole part and the fraction part.


58%283%2F3%29%2B2%2F3 Multiply 58 by 3%2F3 (to get equal denominators)


174%2F3%2B2%2F3 Multiply


%28174%2B2%29%2F3 Add the fractions


176%2F3 Combine like terms.


So 58%262%2F3=176%2F3

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Now let's convert 18%261%2F2 into an improper fraction

18%261%2F2 Start with the second fraction


18%2B1%2F2 Break up the mixed fraction into a sum of the whole part and the fraction part.


18%282%2F2%29%2B1%2F2 Multiply 18 by 2%2F2 (to get equal denominators)


36%2F2%2B1%2F2 Multiply


%2836%2B1%29%2F2 Add the fractions


37%2F2 Add


So 18%261%2F2=37%2F2


So the length and width as improper fractions are 176%2F3 and 37%2F2. In other words, L=176%2F3 and W=37%2F2


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=%28176%2F3%29%2837%2F2%29%283%2F4%29 Plug in L=176%2F3, W=37%2F2 and H=3%2F4


V=%28176%2A37%2A3%29%2F%283%2A2%2A4%29 Combine the fractions (note: just multiply the corresponding numerators and denominators)


V=%2822%2A2%2A4%2A37%2A3%29%2F%283%2A2%2A4%29 Factor 176 into 176=88%2A2=22%2A2%2A4


Cancel out the common terms.


V=22%2A37 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

So...




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.