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Question 658778: Rate 1 $42 plus $.12 mile
Rate 2 $84 plus .06 mile
How many miles must one drive to pay less than Rate 2
how do I work this problem
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! plan a = 42 + .12*x
plan b = 84 + .06*x
x represents the number of miles driven.
you want to find the number of miles that has to be driven in order for r.1 to be less than r.2
set your equation as:
cost for plan a < cost for plan b
since cost for plan a = 42 + .12*x and cost for plan b = 84 + .06*x, your equation becomes:
42 + .12*x < 84 + .06*x
you want to solve for x.
subtract 42 from both sides of the equation to get:
.12*x < 84 + .06*x - 42
subtract .06*x from both sides of the equation to get:
.12*x - .06*x < 84 - 42
combine like terms to get:
.06*x < 42
divide both sides of the equation by .06 to get:
x < 42 / .06 which becomes x < 700
if the number of miles driven is less than 700 then cost for plan a will be less than cost for plan b
if the number of miles driven is equal to or greater than 700 then cost for plan a will be greater than or equal to cost for plan b
the following table shows the number of miles driven and the cost for plan a compared to the cost for plan b.
number of miles driven
cost for plan a
cost for plan b
699 125.88 125.94
700 126 126
701 126.12 126.06
at 699 miles, plan a costs less than plan b
at 700 miles, plan a and plan b cost the same.
at 701 miles, plan a is more expensive than plan b.
if the miles driven are less than 700, plan a will always cost less than plan b.
if the miles driven are greater than 700, plan a will always cost more than plan b.
you may substitute different miles to confirm for yourself that this is accurate.
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