Andrew M. answered • 03/30/16
Tutor
New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors
Cost will be a function of miles driven.
Company A; C(m) = $150 + $.50 per mile
C(m)= 150 + .5m
Company B; C(m) = $60 + $.80 per mile
C(m) = 60 + .8m
We want to know for what value of m the rental cost for
Company A is less than rental cost for Company B
150 + .5m < 60 + .8m
We need to get all the variables on one side of the inequality.
Subtract .5m from both sides.
150 + .5m - .5m < 60 + .8m - .5m
150 < 60 + .3m
We now have all the variables consolidated on one side.
We need to get the constants on the other side.
Subtract 60 from both sides.
150 - 60 < 60 + .3m - 60
90 < .3m
Now the variable is isolated on one side. EXCEPT that it
is multiplied by .3 We need the "m" to be just a single
m with nothing added or subtracted to/from it or
multiplied/divided by it. Since we have .3m which is
m multiplied by .3, we need to divide both sides by .3
90/.3 < .3m/.3
300 < m
We can turn this inequality around, just remembering
that the open side of the inequality faces the m
m > 300
If we drive more than 300 miles in a day, the rental cost for
Company A is less than the rental cost for Company B.
You can plug in a couple of values for m in your original equations
to verify.
Let's try m = 310
Company A; C(310) = 150 + .5(310) = $305
Company B; C(310) = 60 + .8(310) = $308
This fits
Let's look at a value of m less than 300. Try m = 250
Company A; C(250) = 150 + .5(250) = $275
Company B; C(250) = 60 + .8(250) = $260
Our answer works. For m under 300 miles Company B is cheaper
and for m over 300 miles Company A is cheaper.
Just FYI. At m=300 the costs are equal at $300 for either company.
