10. An item is originally priced at $75. It is marked down 30% the first week but still does not sell. It is then further discounted 20% and sells to a nice couple from Chicago.
a) At what price did the item finally sell for?
b. If sales tax is 9 %%, how much did the couple pay altogether for the item?

A. 37.50

B. 40.87

Step-by-step explanation:

75.00x50%=37.50

37.50×9%=3.37

37.50+3.37=40.87

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0