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16 August, 21:29

Alex sells T-shirts. It costs Alex $6.50 to buy each T-shirt. Alex also pays $150 each month to rent equipment to add print to the T-shirts. Alex sells each T-shirt for $12. Write an inequality that can be used to determine the number of T-shirts (T) Alex must sell each month in order to make a profit for the month.

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  1. 17 August, 01:10
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    Making a profit means ending the month with a number above 0, so your inequality will have to be greater than 0.

    (sell) t-shirt = 12

    (make) t-shirt = 6.50

    and a constant of 150

    so your current equation will be the cost of making a t-shirt, the money received by selling, and the cost of rent. it'll look like:

    12t - 6.50t - 150 > 0

    but you want to get t alone to know how many t-shirts you have to sell, so solve the inequality:

    12t - 6.50t - 150 > 0

    12t - 6.50t > 150

    5.50t > 150

    t > (150/5.50)

    and that fraction is roughly 27.27, so you'll round it up to the next whole number because alex can't make/sell a twenty-seventh of a t-shirt.

    alex will have to make 28 t shirts to make a profit, and you can plug it back into the equality like so to check it:

    12t - 6.50t - 150 > 0

    12 (28) - 6.50 (28) - 150 > 0

    336 - 182 - 150 > 0

    4 > 0

    and that statement is true, measly profit as it is.
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