SOLUTION: Write an inequality for the problem and determine the constraints on the variables. Then use your inequality to answer the question. Show all your work and explain your reasoning.

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Question 864890: Write an inequality for the problem and determine the constraints on the variables. Then use your inequality to answer the question. Show all your work and explain your reasoning.
Company A charges a $5 fee plus $0.20 per ounce to ship a medium sized package to a nearby city. Company B charges a $10 fee plus $1.00 per 100 miles for the same shipment. Amit has determined that it will cost less to ship his package using company B. Is Amit's conclusion accurate?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Company A:
5%2B0.2%2Ax, using x for how many OUNCES

Company B:
10%2B1%2Ad, using d for how many MILES

x must be greater than 0, and d must be greater than or equal to 0.
The given determination made was B costs less than A:
10%2Bd%3C5%2B0.2x
5%2Bd%3C0.2x
The left member is for using company B, and the right member is for using company A. Amit has no assurance that company B costs less than company A. Imagine the example, a package to be delivered to d=0, and package size of x=100 ounces. The example shows 5%3C20 which is true. Imagine another example, d=0 and x=25 ounces. For this, 5%3C5 is false; and for x%3C25 will also be false. Amit would guess wrongly for some combinations d and x, and correctly for some others. His conclusion depends on his particular distance and size of package.