Algebra Linear models

Question

A T-shirt company charges your team an initial fee of $25 to create the teams design. Each T-shirt printed with your design costs an additional $8.

Part a) Wrote a linear model that represents the total cost of purchasing your teams T-shirts with your design as a function of the number of T-shirts

Part B.) Your team has 35 members. If a T-shirts is purchased for every member, what would the cost be?

Answer 1

Part A) This situation can be modeled with linear function. First you need to identify your initial value, or starting cost. This is the cost if no shirts are made. If no shirts are made, there is still the cost of $25 for making the logo. The next thing that needs to be found is the rate of change. This is how much the price will go up for each shirt made. This is $8. This information can then be put in to slope intercept form:

f(x) = mx +b

Your slope or rate of change is m and the y-intercept or initial value is b. Substitute the values in.

f(x) = 8x + 25.

This is the cost of making x shirts.

Part B)

Given that f(x) = 8x +25 gives the price for x shirts, we can find the price for 35 shirts with substitution.

f(35) = 8(35) + 25

Then multiply and add.

f(35) = 280 + 25, f(35) = 305

It will cost $305 to make a shirt for each of the 35 members.

Answer 2

Part (a) Asks you to write a linear model, which means you must write an equation of the form y = mx + b.

In this case, "x" is going to be the number of T-shirts, because that is the variable that changes according to your whim (it's the independent variable)

"y" is going to be the cost, because it depends on the number of T-shirts you make (y is the dependent variable)

Since the initial fee is $25, this means they will charge this to you once and never charge you this again (or so you hope). So the "b" must equal $25.

Then the prompt says that "each T-shirt costs an additional $8".

$8 "EACH" means that you will multiply $8 to the number of T-shirts, x. The word "additionally" implies you will add 8x to the initial fee, so ..... (drumroll please)

The linear model is y = 8x + 25.

I'm sure that you're teacher would rather you use "C" for cost and "t" for the number of T-shirts, so if you really want to gain some brownie points, you can use

C= 8t + 25

Now for part (b). Well, since you figured out the linear model in part (a) and we know that t is the number of T-shirts, then we only need to substitute t = 35 into our linear model to obtain the cost, C.

C = 8(35) + 25 = 305

It will cost $305 dollars to make 35 T-shirts.

(teachers also love it when you write the answer in a complete sentence)