```Question 128006
The trick is to find the number of hours where the two companies would charge the same amount.  So if the expression for HL is {{{80+35h}}} and the expression for QM is {{{55h}}}, you need to set these two expressions equal to each other and solve for h:

{{{55h=80+35h}}}
{{{55h-35h=80}}}
{{{20h=80}}}
{{{h=4}}}

So now we know that at 4 hours, it doesn't matter which company you choose:

{{{80+35(4)=80+140=220}}} and {{{55(4)=220}}}.

From the first two parts of the problem, you know that QM is a better deal at some point less than 4, and HM is a better deal at a point greater than 4.

So your inequality becomes: QM is a better deal if {{{h<4}}}.  Notice that we don't include the 'or equal to' in the inequality because we are looking for QM to be a BETTER deal.  If {{{h=4}}} then QM and HL offer the same deal, and the same is not better.

This brings up another point.  Could we have said that QM is a better deal if {{{h<=3}}}?  Actually, we can't answer that with the information given, because we don't know whether either company charges a fractional hourly rate for a fraction of an hour used.

If, for example, QM charges \$55 for every hour or part of an hour, i.e. 3.5 hours is the same fee as 4 hours, then {{{h<=3}}} would be the same as {{{h<4}}}.  On the other hand, if they actually charge {{{55(3.5)=192.5}}} for 3.5 hours of use, then the only acceptable answer is {{{h<4}}}.

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