Question

Kevin wants to buy an area rug for his living room. He would like the area rug to be no smaller that 48 square feet and no bigger than 80 square feet. If the length is 2 feet more than the width, what are the range of possible values for the length?

Answer 1

8-10 feet

Explanation:

If the length of the carpet is two more than the width, the width can be expressed as x and the length can be expressed as x+2. This means that the area(x^2+2x) must be greater than 48 but no less than 80.

Now we can solve for both the maximum and minimum cases:

x^2+2x=48, x^2+2x-48=0, now we can factor, (x+8)(x-6)=0, and now we can use the Zero Product Property to find x=-8;x=6. Since we cant have negative width, x at least has to be equal to 6.

x^2+2x=80,x^2+2x-80=0, now we can factor, (x+10)(x-8), and now using the Zero Product Property to find x=-10;x=8, and since it must be positive, at most x can equal 8.

Now since the length is two more than the width, x, you add two to both of these values and get a range of 8-10 feet.