Question

16)a) write an equation that can be used to answer the question, andb) use a quadratic solving method to answer the questionThe senior class buys shirts to wear for a pep rally. The cost of the shirts can be modeled by the formula C = 0.15? + 2.4s + 25 where C is the total cost for purchasing s shirts. Use the quadratic formula to determine how many shirts can be purchased for $430?

Answer 1

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:

`\begin{gathered} x=(-b\pm√(b^2-4ac))/(2a) \\ \\ x=(-2.4\pm√((2.4)^2-4(0.1)(-405)))/(2(0.1)) \\ \\ x=(-2.4\pm√(5.76+162))/(0.2) \\ \\ x=(-2.4\pm√(167.76))/(0.2) \\ \\ x=(-2.4\pm12.95)/(0.2) \\ \\ x=(-2.4+12.95)/(0.2),(-2.4-12.95)/(0.2) \\ \\ x=(10.55)/(0.2),(-15.35)/(0.2) \\ \\ x=52.75 \end{gathered}`

We will only take the positive value of x.

Which comes out to be 52.75, so we can buy 52 shirts from $430.