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Question 1109909: Clintonville Landscapers (CL) Charges a delivery fee of $30 regardless of the amount of mulch delivered within a 20mile radius. The cost of Absolute Black Ultra mulch is $39.99 per cubic yard at CL. Oregonia Nursery is having a special and charges $28.49 for the same mulch, but their delivery charge is $50 per transaction. For how many cubic yards is buying mulch from Oregonia Nursery cheaper? Round your answer to the nearest tenth.
So, that is the question. I know how to solve an inequality such as a flat rate + $ per mile (as an example) with only a certain dollar amount I'm able to spend. Not sure how to approach this one though.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! clintonville landsacpers charges 30 dollars regardless of the amount of mulch delivered within a 20 mile radius.
looks like oregonia charges 50 dollars regardless of the amount of mulch delivered.
i believe the built in assumptions are that both are charging a flat fee per transaction within a 20 mile radius.
that makes clintonvolle charge 30 + 39.99 * x and oregonia charge 50 + 28.99 * x, where x is equal to the cubic yards delivered.
therefore, the break even point would be when 30 + 39.99 * x = 50 + 28.99 * x.
since you want to know when the cost at clintonville is greater than the cost at oregonia, then the equation becomes the following inequality.
30 + 39.99 * x > 50 + 28.99 * x.
subtract 30 from both sides of this inequality and subtract 28.99 * x from both sides of this inequality to get:
39.99 * x - 28.99 * x > 50 - 30
combine like terms to get:
11 * x > 20.
solve for x to get:
x > 20 / 11 = 1.818181818
the cost using clintonville will be greater than the cost using oregonia when more than 1.818181818 cubic yards of black ultra mulch are delivered.
conversely, the cost using oregonia will be less than the cost using clintonville when more than 1.818181818 cubic yards of black mulch are delivered.
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