Question

Jill would like an increase in the hourly wage she receives from the Mathematics Research Center, where she works in the mail room. Her boss gives her an equation to solve, telling her that her raise is the solution to the equation, but only if she can solve it. The equation is x 2- 6x + 9 = 0. What was the amount of her raise per hour? Answer:

Answer 1

Answer:

Jill will receive an increase of $3 per hour

Step-by-step explanation:

The Quadratic Equation

The quadratic equation can be represented in the standard form as:

$ax^2+bx+c=0$

being a,b, and c are constants.

It can be solved by using the quadratic formula:

$\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Jill would like an increase in her hourly wage. The increase will come as the solution for a maths equation.

She must solve the equation:

$x^2-6x+9=0$

The solution to the equation, or value of x, is the increase in her hourly wage.

Comparing with the general form, we have a=1, b=-6, c=9. Thus, the solutions are:

$\displaystyle x=\frac{-(-6)\pm \sqrt{(-6)^2-4(1)(9)}}{2(1)}$

$\displaystyle x=\frac{6\pm \sqrt{36-36}}{2}$

$\displaystyle x=\frac{6\pm \sqrt{0}}{2}$

The square root is 0, therefore is only one solution:

$\displaystyle x=\frac{6}{2}=3$

x = 3

Thus, her raise per hour is $3.