Question

The width of a yard is four less than a number. The length is five more than twice that same number. The area of the yard is 15 meters. Write and solve a quadratic equation to find the value of X; then choose the answer that best describes the value of X

Answer 1

Let's denote the number as x.

According to the problem, the width of the yard is four less than the number x, which can be expressed as x - 4.

The length of the yard is five more than twice the number x, which can be expressed as 2x + 5.

The area of the yard is calculated by multiplying the width and the length, so we have the equation:

(x - 4)(2x + 5) = 15

Expanding the left side of the equation gives:

2x^2 + 5x - 8x - 20 = 15

Combine like terms:

2x^2 - 3x - 20 = 15

Rearrange the equation to standard quadratic form:

2x^2 - 3x - 35 = 0

Now we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use factoring:

(2x + 7)(x - 5) = 0

Setting each factor equal to zero:

2x + 7 = 0 or x - 5 = 0

Solving each equation:

2x = -7 or x = 5

Dividing by 2 in the first equation:

x = -7/2 or x = 5

Therefore, the possible values for x are -7/2 or 5. The answer that best describes the value of x is 5.