Question

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1. the total cost of two t - shirt companies based on the number of shirts ordered is shown below.

(there is a graph here with x - axis labeled # shirts (from 0 to 10) and y - axis labeled total cost ($) (from 0 to 30), with two lines: company a and company b)
a. write an equation to represent each company.
b. how many shirts would need to be ordered for the cost to be the same at either company? what would the total cost be?
c. if justin needs to order 5 shirts, which company would be the cheaper option?

Explanation:

Part a:

Step1: Find Company A's equation

Company A's line passes through (0,0) and (3,9). Slope $m=\frac{9-0}{3-0}=3$. Equation: $y=3x$

Step2: Find Company B's equation

Company B's line passes through (0,6) and (3,9). Slope $m=\frac{9-6}{3-0}=1$. Equation: $y=x+6$

Part b:

Step1: Set equations equal

$3x = x + 6$

Step2: Solve for x

$3x - x = 6$
$2x = 6$
$x = 3$

Step3: Find total cost

Substitute $x=3$ into $y=3x$: $y=3\times3=9$

Part c:

Step1: Calculate cost for Company A

$y=3\times5=15$

Step2: Calculate cost for Company B

$y=5+6=11$

Step3: Compare the two costs

$11 < 15$, so Company B is cheaper.

Answer:

a. Company A: $y=3x$; Company B: $y=x+6$
b. 3 shirts, total cost is $\$9$
c. Company B