Word Problems: finding eqns for cost of producing T-shirts

[Tigertigre2000]

Highlander Screen Printers received two orders for a special T-shirt for a mathematics symposium. The first order was for 40 shirts at a total cost of $292. The second order was for 80 shirts at a total cost of $552. Each order included a standard shipping and handling charge.

A) Write a linear equation to represent the cost function.
B) What is the cost per shirt?
C) What is the standard shipping and handling charge?

I'm totally lost. I don't know how to set up this problem. or how to get parts B) and C). (I'm not very good at word problems. I work better when I have an equation.)

Thanks; I appricitate your help!

 

[Mrspi]

Re: Word Problems: finding eqns for cost of producing T-shir

Highlander Screen Printers received two orders for a special T-shirt for a mathematics symposium. The first order was for 40 shirts at a total cost of $292. The second order was for 80 shirts at a total cost of $552. Each order included a standard shipping and handling charge.

A) Write a linear equation to represent the cost function.
B) What is the cost per shirt?
C) What is the standard shipping and handling charge?

I'm totally lost. I don't know how to set up this problem. or how to get parts B) and C). (I'm not very good at word problems. I work better when I have an equation.)

Thanks; I appricitate your help!

Let x = number of t-shirts
Let y = cost

Now, the problem gives you the coordinates of two points (x, y): (40, 292) and (80, 552).

For part A, start by finding the slope of the line through (40, 292) and (80, 552). The formula for finding slope of the line through (x<SUB>1</SUB>, y<SUB>1</SUB>) and (x<SUB>2</SUB>, y<SUB>2</SUB>) is

m = (y<SUB>2</SUB> - y<SUB>1</SUB>) / (x<SUB>2</SUB> - x<SUB>1</SUB>)

Substitute the coordinates of the two points:

m = (552 - 292) / (80 - 40)

m = 260/40

m = 6.5

You can begin to write the equation of the line in slope-intercept form:
y = mx + b
y = 6.5x + b

The next step is to find the value of b. Pick one of the points, say (40, 292). Substitute 40 for x and 292 for y:
292 = 6.5(40) + b
292 = 260 + b
32 = b

You can now complete the equation by substituting 32 for b:

y = 6.5x + 32

Ok.....I did the hard part for you. Can you answer parts B and C now?