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

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) (Show Source): You can put this solution on YOUR website!
# 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 into an improper fraction

Start with the first fraction

Break up the mixed fraction into a sum of the whole part and the fraction part.

Multiply 58 by (to get equal denominators)

Multiply

Add the fractions

Combine like terms.

So

-----------------------------

Now let's convert into an improper fraction

Start with the second fraction

Break up the mixed fraction into a sum of the whole part and the fraction part.

Multiply 18 by (to get equal denominators)

Multiply

Add the fractions

Add

So

So the length and width as improper fractions are and . In other words, and

Now remember, the volume of a rectangular block is

where L is the length, W is the width, and H is the height

Plug in , and

Combine the fractions (note: just multiply the corresponding numerators and denominators)

Factor into

Cancel out the common terms.

Simplify

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.

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