Question

Janna has finished weaving a blanket. She made the length of the blanket 1 foot greater than twice its width, because otherwise her toes get cold. If the area covered by the blanket is

Answer 1

Explanation:

length of blanket × width of blanket = (2a + 1)(a) = 2a2 + a.

Since we’re told the area covered by the blanket is 28 square feet, we know that

2a2 + a = 28.

To solve this equation, we need to rearrange the terms so that we have a polynomial set equal to 0:

2a2 + a – 28 = 0.

Then we factor:

(2a – 7 )(a + 4) = 0.

The two solutions to this equation are a = 3.5 and a = -4. a = -4 sure doesn’t make sense, because we can’t have a blanket that’s -4 feet wide. That won’t cover even one of Janna’s toes. The blanket must be 3.5 feet wide.

To find the length, we plug the width 3.5 in for a in the expression 2a + 1. The length of the blanket is

2(3.5) + 1 = 8 feet

We can easily check our answers by multiplying the width and length of the blanket, and seeing if we do end up with 28.

(3.5)(8) = 28