Speedy Printing charges $23 for 200 deluxe business cards and $35 for 500 deluxe business cards. Give that the cost is a linear function of the number of cards printed, find a formula for that function and find the cost of 700 business cards.
Someone please help me with this!
To find the formula for the cost of printing deluxe business cards, we can create a linear equation using the given information.
Let's define the cost of printing deluxe business cards as C and the number of cards as N. We will use the points (200, 23) and (500, 35) to determine the equation.
First, let's find the slope of the line, which represents the rate of change in cost per card:
slope = (change in cost) / (change in cards)
= (35 - 23) / (500 - 200)
= 12 / 300
= 0.04
Next, we can use the point-slope equation of a line to find the equation:
C - 23 = 0.04(N - 200)
Expanding the equation, we get:
C - 23 = 0.04N - 8
Rearranging the equation to solve for C, we have:
C = 0.04N + 23 - 8
C = 0.04N + 15
Therefore, the formula for the cost of printing deluxe business cards is C = 0.04N + 15.
Now, let's find the cost of printing 700 business cards by substituting N = 700 into the equation:
C = 0.04(700) + 15
C = 28 + 15
C = 43
Therefore, the cost of printing 700 deluxe business cards would be $43.