SOLUTION: The costs C and income I for making and selling T-shirts with a school logo are given by the equations C=$535+4.50n and I=$12n, where n is the number of T-shirts. a. How many T-

Question 568280: The costs C and income I for making and selling T-shirts with a school logo are given by the equations C=$535+4.50n and I=$12n, where n is the number of T-shirts.
a. How many T-shirts must be bought and sold to break even? Explain. I got that the answer to this one is $72 as you cannot make 71.3 shirts.
b. Suppose only 50 shirts are sold. Is there a profit or loss. I said Loss.
C. Suppose the income is $1,200. Is there a profit or loss. I said profit.
WHERE I NEED HELP
d. i. For each equation, find the coordinates of a point that lies on the graph of the equation.
ii. What information does this point give?
iii. Describe how to use the equation to see that the point will be on the graph.
I can't remember how to put these equations on a graph.
Please help. Thank you
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The costs C and income I for making and selling T-shirts with a school logo are given by the equations C=$535+4.50n and I=$12n, where n is the number of T-shirts.
a. How many T-shirts must be bought and sold to break even? Explain. I got that the answer to this one is $72 as you cannot make 71.3 shirts.
C=$535+4.50n and I=$12n
535+4.5n = 12n
535 = 6.5n
n = 72 when rounded up
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b. Suppose only 50 shirts are sold. Is there a profit or loss. I said Loss.
OK
-----------------------
C. Suppose the income is $1,200. Is there a profit or loss. I said profit.
So n would be 100 : So profit.
----------------------------
WHERE I NEED HELP
d. i. For each equation, find the coordinates of a point that lies on the graph of the equation.

ii. What information does this point give?
That is the equilibrium point (72,864).
That is where I = C
------------------------
iii. Describe how to use the equation to see that the point will be on the graph.
Replace n and C with the numbers
Replace n = I with the numbers
Since (72,864) satisfies both equations that
point is the solution for the system of
two equations.
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Cheers,
Stan H.
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