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Question 1189196: Gus plans to sell a limited number of T-shirts printed with a design he made. It costs him $690 to purchase the unprinted T-shirts and the screen printing supplies he needs to produce his finished product. He prints 50 shirts, and is sure he will sell them all because his designs are in high demand. He wants his profit (the difference between his sales revenue and his expenses) to be at least 60% of his expenses. If he will only sell his shirts for a whole dollar amount (for example, $8.00), what is the lowest price Gus can set for the shirts?
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
Gus plans to sell a limited number of T-shirts printed with a design he made.
It costs him $690 to purchase the unprinted T-shirts and the screen printing supplies
he needs to produce his finished product. He prints 50 shirts, and is sure he will sell
them all because his designs are in high demand. He wants his profit
(the difference between his sales revenue and his expenses) to be at least 60% of his expenses.
If he will only sell his shirts for a whole dollar amount (for example, $8.00),
what is the lowest price Gus can set for the shirts?
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Let x be that lowest price per shirt, in integer number of dollars.
The lowest price will be provided, if he sells all 50 shirts.
So, we write inequality as we read the problem
50x >= 1.6*690.
Now express x and find it
x >=  = 22.08 dollars.
Since we want to get integer value for x, we round 22.08 to the nearest greater integer value, which is 23.
ANSWER. Under the imposed condition, the lowest price is 23 dollars per shirt.
Solved and explained.
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