Question

1. the drama club is printing t - shirts for its members. the printing company charges a certain amount for each shirt plus a setup fee of $40. there are 21 students in the drama club.

a. if there are 21 students in the club and the t - shirt order costs a total of $187, how much does each t - shirt cost?
b. the equation ( f + 6.50(21)=201.50 ) represents the cost of printing the shirts at a second printing company. find the solution to the equation and explain what the solution means in the context of the problem.

Explanation:

Step1: Solve part a

Let the cost of each T - shirt be \(x\). The total cost is the cost of 21 T - shirts plus the setup fee. So the equation is \(21x + 40=187\).
Subtract 40 from both sides: \(21x=187 - 40\), so \(21x = 147\).
Divide both sides by 21: \(x=\frac{147}{21}=7\).

Step2: Solve part b

Given the equation \(f + 6.50(21)=201.50\).
First, calculate \(6.50\times21 = 136.5\).
The equation becomes \(f+136.5 = 201.50\).
Subtract 136.5 from both sides: \(f=201.50 - 136.5\), so \(f = 65\).

In the context of the problem, \(f\) represents the setup fee of the second printing company.

Answer:

a. Each T - shirt costs \(\$7\).
b. The solution \(f = 65\) means that the setup fee of the second printing company is \(\$65\).