Given:
C = 0.1s² + 2.4s + 25
(C is the cost of purchasing s shirts)
To find:
We need to use the quadratic formula to determine how many shirts can be purchased for $430.
Step by step solutions:
Let's say we want to buy 1 shirt,
Cost of buying 1 shirt (S =1) = 0.1s² + 2.4s + 25
Cost of buying 1 shirt (S =1) = 0.1 + 2.4 + 25
Cost of buying 1 shirt (S =1) = 27.5
If we want to know, how many shirt can be purchased from $430, we will equate it to 430.
0.1s² + 2.4s + 25 = 430
0.1s² + 2.4s - 405 = 0
We will use the quadratic formula to solve this problem:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ x=\frac{-2.4\pm\sqrt{(2.4)^2-4(0.1)(-405)}}{2(0.1)} \\ \\ x=\frac{-2.4\pm\sqrt{5.76+162}}{0.2} \\ \\ x=\frac{-2.4\pm\sqrt{167.76}}{0.2} \\ \\ x=\frac{-2.4\pm12.95}{0.2} \\ \\ x=\frac{-2.4+12.95}{0.2},\frac{-2.4-12.95}{0.2} \\ \\ x=\frac{10.55}{0.2},\frac{-15.35}{0.2} \\ \\ x=52.75 \end{gathered}[/tex]
We will only take the positive value of x.
Which comes out to be 52.75, so we can buy 52 shirts from $430.
