48.1k views
3 votes
Gerald purchases a rectangle plot of land The length of the plot is 20 feet more than the width. The cost of the land was $12 per square foot. Gerald also had a fence put around the entire perimeter of the plot, at a cost of $8 per linear foot. The total amount he spent on both the land and the fence was $10,560.

Write an equation in one variable that can be used to find the width, x feet, of the plot. Express the equation in the form ax^2 + bx + c = 0. Provide evidence to support your answer.

User EXXL
by
8.2k points

1 Answer

9 votes

Answer:


12x^(2)+272x+320=10560

Explanation:

Start by setting the width = x.

Length is equal to x+20.

We know the cost of the land was $12 per square foot (area) and the cost of the fence around the perimeter is equal to $8 per foot. This gives us two equations we need to work with.

$12(x*(x+20)) + $8((2*x)+(2*(x+20))) = 10560. It looks a little difficult to read but as we distribute the cost throughout the equations, we see it start to take shape.

12(x^2+20x) + 8(2x+2x+40) = 10560

12x^2+240x+16x+16x+320 = 10560

12x^2+272x+320=10560

The roots of our equation here are x=20, and x = -128/3

Since we know that area is not negative, our answer is x=20.

Check the work: 12(20)^2 + 272(20) +320 = 10560

User Knack
by
9.1k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories