Question

Cameron is designing a calendar as a fund raising project for math class. The cost of printing is $500, plus $2.50 per calendar. Write an equation in slope intercept form that models the total cost of printing the calendar. Each calendar will sell for 5.00 each. Write an equation to model the total income , y , for selling x calendar

Answer 1

The equation to model the total cost of printing the calendar is y = 500 + 2.50x and the equation to model the total income for selling x calendars is y = 5x.

Step-by-step explanation:

To write an equation in slope-intercept form that models the total cost of printing the calendar, we need to consider the fixed cost and the cost per calendar. The fixed cost is the cost of printing without any calendars, which is $500. The cost per calendar is $2.50. So, the equation can be written as:

y = 500 + 2.50x

In this equation, y represents the total cost and x represents the number of calendars.

To write an equation to model the total income for selling x calendars, we need to consider the selling price per calendar. Each calendar sells for $5. So, the equation can be written as:

y = 5x

In this equation, y represents the total income and x represents the number of calendars sold.

Answer 2

The correct answers are:

y = 2.50x + 500; and y = 2.50x - 500

Explanation:

In the first equation, x represents the number of calendars printed and y represents the total cost. Each calendar costs $2.50 to print; this gives us the expression 2.50x. We also have the $500 fee for printing, which gives us 2.50x + 500. This is the total cost of printing, which is represented by y:

y = 2.50x + 500

For the second equation, x is the number of calendars sold and y is the total income. Each calendar sells for $5; this gives us 5x. However, we must take away the cost of printing. We already know from the previous equation that the expression for the cost of printing is 2.50x+500; we take this away from 5x and have

y = 5x-(2.50x+500)

Distributing the subtraction sign, we have

y = 5x-2.50x-500

Combining like terms, we have

y = 2.50x-500