Question 457198: When writing an inequality for a word problem, do the units have to be converted to have the same value (dollars and cents) before writing the expression? This was one of our homework questions
A cell phone company has offered you two different rates. The first rate is $35 per month and 5 cents per phone call (time does not matter). The second offer is $55 per month and 2 cents per call. Set up the inequality to model this problem and find where it is less expensive to go with the second plan.
This is the inequality I came up with: 35 + 5x < 55 + 2x, but I'm not sure if that's correct. Since the price per call is in cents and not whole dollars, would I need to somehow convert that value before trying to write up the inequality? And if so, would it be something like: 35 + .05x < 55 + .02x ? Any help on this would be greatly appreciated. Thank you.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 35 + .05x < 55 + .02x
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Yes, you need the decimals so everything
is stated in terms of dollars.
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But you need to reverse the inequality
because you want the 2nd plan to be
less expensive:
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Solve: 35 + .05x > 55 + .02x
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0.03x > 20
x > 20/0.03
x > 666.67
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2nd plan is less expensive if 667 phone calls are made.
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Cheers,
Stan H.
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