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Levi must paint the inside of his house, the inside of his house has a paintable surface area of...

Question:

Levi must paint the inside of his house, the inside of his house has a paintable surface area of {eq}\rm 3500\ ft^2 {/eq}. Levi went to the European "Home Depot" to buy his paint when he returned home, he realized each bucket of paint covers {eq}\rm 5\ m^2 {/eq}, Levi has {eq}140 {/eq} buckets of paint.

A. How many buckets of paint will it take to cover the inside of Levi's house with 2 coats of paint?

B. If any, how many buckets of paint will be left over and how many square feet will leftover paint cover?

Relationship between sq.feet and sq.meter:

The relationship between sq.ft and sq. meter is given as;

{eq}1 ft^2 = 0.093 m^2 {/eq}

If x relates to y as x directly proportional to y then the new value of y viz. y' corresponding to x' can be found as:

{eq}y' = \displaystyle \frac{x \cdot y}{x'} {/eq}

Answer and Explanation:

a) To find the bucket of paint that it will take to cover Levi's house in 2 coats of paint

Total surface area for two coat of paint will be

{eq}= 3500 \times 2\\ = 7000 \: ft^2 {/eq}

Given that,

Quantity present in each bucket of paint can cover an area of

{eq}= 5 \: m^2\\ = 5 \displaystyle \frac{1}{0.093}\\ = 53.81 \: ft^2 {/eq}

Therefore, the number of buckets required to cover the area in 2 coats of paint will be

{eq}= \displaystyle \frac{7000}{53.81}\\ = 130.08\\ \approx 130 {/eq}


b)To find the number of buckets left over and the area that they can cover:

We found that 130 buckets of paint will be used for 2 paint coatings

Therefore, from the total 140 buckets, the net number of buckets left are

{eq}=140-130\\ = 10 {/eq}

We know that each bucket covers an area of {eq}53.81 \: ft^2 {/eq}

Therefore, the total area that 10 bucket of paint can cover is

{eq}= 10 \times 53.81\\ = 538.1 \: ft^2 {/eq}


Learn more about this topic:

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Directly Proportional: Definition, Equation & Examples

from High School Algebra II: Help and Review

Chapter 1 / Lesson 23
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