Questions: Fall 2024 (41084) Section 3.7 Homework Question 12, MLM Only 3.7.22 Part 5 of 5 A printer charges 2.20 for binding plus 5 cents per page for each copy of a community group's annual report. Write the cost equation and answer the following questions. What is the fixed cost? 2.20 (Simplify your answer. Type an integer or a decimal.) What is the variable cost? 0.05 (Simplify your answer. Type an integer or a decimal.) Let y represent the cost of the annual report and x represent the number of pages. What is the cost equation? y=0.05x+2.20 (Simplify your answer.) What will it cost to produce a 27 page report? 3.55 (Simplify your answer. Type an integer or a decimal.) If the report cost was 3.70, the report is pages. (Simplify your answer. Type an integer or a decimal.)

Solution Steps

To solve the given problem, we need to use the cost equation provided and perform some basic arithmetic operations. The cost equation is \( y = 0.05x + 2.20 \), where \( y \) is the total cost and \( x \) is the number of pages.

1. To find the cost of producing a 27-page report, substitute \( x = 27 \) into the cost equation.
2. To find the number of pages when the cost is \$3.70, solve the equation \( 3.70 = 0.05x + 2.20 \) for \( x \).

To find the cost of producing a 27-page report, we use the cost equation:

\[ y = 0.05x + 2.20 \]

Substituting \( x = 27 \):

\[ y = 0.05(27) + 2.20 = 1.35 + 2.20 = 3.55 \]

Thus, the cost to produce a 27-page report is:

\[ \boxed{y = 3.55} \]

To find the number of pages when the total cost is \$3.70, we set up the equation:

\[ 3.70 = 0.05x + 2.20 \]

Subtracting the fixed cost from both sides:

\[ 3.70 - 2.20 = 0.05x \]

This simplifies to:

\[ 1.50 = 0.05x \]

Now, solving for \( x \):

\[ x = \frac{1.50}{0.05} = 30 \]

Thus, the number of pages for a report costing \$3.70 is:

\[ \boxed{x = 30} \]

Final Answer