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

Her raise per hour is $3.

Explanation:

Quadratic Equation

The standard representation of a quadratic equation is:

`ax^2+bx+c=0`

where a,b, and c are constants.

It can be solved by using the quadratic formula:

`\displaystyle x=(-b\pm √(b^2-4ac))/(2a)`

Jill asks for an increase in the hourly wage she receives. Since she works in a Maths Center, the increase comes as a maths equation.

She must solve the equation:

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

The solution to the equation 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=(-(-6)\pm √((-6)^2-4(1)(9)))/(2(1))`

`\displaystyle x=(6\pm √(36-36))/(2)`

`\displaystyle x=(6\pm √(0))/(2)`

Since the square root is 0, there is only one solution:

`\displaystyle x=(6)/(2)=3`

x = 3

Thus, her raise per hour is $3.