Algebra 2 - Quadratic Formula

Question

Fundraising: Your class is selling boxes of flower seeds as a fundraiser. The total profit p depends on the amount x that your class charges for each box of seeds. The equation p = -0.5x² + 25x - 150 models the profit of the fundraiser. What's the smallest amount, in dollars, that you can charge and make a profit of at least $125?

When I substitute for p I get:

125 = -0.5x² + 25x - 150

Putting the equation into standard form I get:

-0.5x² + 25x - 275 = 0

where a = -0.5, b = 25, c = -275

When I solve using the quadratic equation, I get:

x = $9.28 or -$59.28

But the answer in the back of the book is $16.34.

Where am I going wrong?

Answer 1

[-25 +or- sqrt( 25^2 - 4(-0.5)(-275) ) ] / [(2)(-0.5)] = <--- plugs into the quadratic formula VERBATIM

[-25+or- sqrt ( 625 - ( -2)(-275))]/[ -1] = <--- half of 4 is 2 and it's negative

[ -25 +or- sqrt ( 625 - 550) ]/(-1) = <--- negative times negative is positive

[ -25+or- sqrt( 75) ] / (-1)

25 -or+ 5*sqrt(3) <---- 75 = 5 * 5 * 3

So the two prices that satisfy this condition are:

33.66+.....

and

16.33

My guess is that you probably ate a negative sign during one of the

first three steps

Answer 2

16.34 is correct.

I have a feeling that you didn't use the quadratic formula correctly.

The quadratic formula ASSUMES that A (the coefficient of the squared term is greater than 0!

Anyway:

-.5x² + 25x - 275 =0

x² - 50x + 550 = 0

Now try the quadratic formula again.