Question

a consulting firm has an initial fee of $300 and charges $150 per meeting. model the total fee f for m meetings.
a. $f = 150m - 300m$
b. $f = 450m$
c. $f = 300 - 150m$
d. $f = 300 + 150m$

a company charges $45 to rent equipment and an additional $10 per day. write the equation for the total cost c for d days of rental.
a. $c = 55d$
b. $c = 45d + 10$
c. $c = 10 - 45d$
d. $c = 45 + 10d$

the total cost for printing a copies of a book is $200 plus $2.50 per copy. which equation represents the total cost (c)?
a. $c = 200a + 2.50$
b. $c = 200 - 2.50a$
c. $c = 200 + 2.50a$
d. $c = 200 \times 2.50$

a gym membership costs $20 per month and a one - time sign - up fee of $30. what equation represents the total cost t after m months?
a. $t = 30m + 20$
b. $t = 20 - 30m$
c. $t = 50m$
d. $t = 20m + 30$

Explanation:

Let's solve each problem one by one:

First Problem (Consulting Firm)

Step 1: Identify Fixed and Variable Costs

Initial fee (fixed cost) = $300, Charge per meeting (variable cost) = $150 per meeting. Total fee \( F \) = Fixed cost + (Variable cost per meeting \( \times \) number of meetings \( m \)).

Step 2: Formulate the Equation

So, \( F = 300 + 150m \) (or \( F = 300 + 150m \), which matches option d).

Second Problem (Equipment Rental)

Step 1: Identify Fixed and Variable Costs

Rental fee (fixed cost) = $45, Additional charge per day (variable cost) = $10 per day. Total cost \( C \) = Fixed cost + (Variable cost per day \( \times \) number of days \( d \)).

Step 2: Formulate the Equation

Thus, \( C = 45 + 10d \) (matches option d).

Third Problem (Printing Cost)

Step 1: Identify Fixed and Variable Costs

Fixed cost = $200, Cost per copy (variable cost) = $2.50 per copy. Total cost \( C \) = Fixed cost + (Variable cost per copy \( \times \) number of copies \( a \)).

Step 2: Formulate the Equation

So, \( C = 200 + 2.50a \) (matches option c).

Fourth Problem (Gym Membership)

Step 1: Identify Fixed and Variable Costs

One - time signup fee (fixed cost) = $30, Monthly cost (variable cost) = $20 per month. Total cost \( T \) = Fixed cost + (Variable cost per month \( \times \) number of months \( m \)).

Step 2: Formulate the Equation

Thus, \( T = 30 + 20m \) (or \( T = 20m+30 \), matches option d).

Answer:

s:

1. For the consulting firm problem: \(\boldsymbol{d}\)
2. For the equipment rental problem: \(\boldsymbol{d}\)
3. For the printing cost problem: \(\boldsymbol{c}\)
4. For the gym membership problem: \(\boldsymbol{d}\)