to rent a certain meeting room, a college charges a reservation fee of $49 and an additional fee of $8.90 per hour. the history club wants to spend less than $129.10 on renting the meeting room. what are the possible amounts of time for which they could rent the meeting room? use T for the number of hours the meeting room in rented and solve your inequality for t.
i think the answer is T is greater than or equal to 9 , but i always get the signs messed up :( please help!

Question

to rent a certain meeting room, a college charges a reservation fee of $49 and an additional fee of $8.90 per hour. the history club wants to spend less than $129.10 on renting the meeting room. what are the possible amounts of time for which they could rent the meeting room? use T for the number of hours the meeting room in rented and solve your inequality for t.
i think the answer is T is greater than or equal to 9 , but i always get the signs messed up :( please help!

jdoe0001 · Answer

how did you get $\bf t \ge 9$ anyway?

anonymous · Answer

$129.10 - 49 = 80.1 / $8.90 = 9

jdoe0001 · Answer

well....
I'd rather put it this way 

they want to spend LESS THAN $129.10
there's a base charge, reservation, of a flat fee of $49
so they have to pay that just to try to get it at all

per hour, they charge is $8.90, so $\begin{array}{llll}
hour&charge
\\hline\
1&8.9(1)\
2&8.9(2)\
3&8.9(3)\
...&....\
t&8.9t
\end{array}$

so they'd end up spending "t hours"
and after "t hours" they'd owe    $\bf 49+8.9t$

and they want THAT to be LESS THAN $129.10

so $\bf 49+8.9t>129.1\implies 8.9t>129.1-49\implies 8.9t>80.1
\ \quad \
t>\cfrac{80.1}{8.9}\implies t>9\ hours$

anonymous · Answer

the correct answer was t<9