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To rent a certain meeting room, a college charges a reservation fee of $49 and an additional fee of $6.70 per hour. The math club wants to spend less than $95.90 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 is rented, and solve your inequality for t.

Respuesta :

The possible amounts of time for which they could rent the meeting room is less than 7

Solution;

To rent a certain meeting room, a college charges a reservation fee of $49 and an additional fee of $6.70 per hour

Let "t" be the number of hours

Therefore,

charge = 49 + 6.70t

The math club wants to spend less than $95.90 on renting the meeting room

Therefore,

[tex]49 + 6.70t< 95.90[/tex]

Solve the inequality

[tex]49+6.7t<95.9\\\\\mathrm{Multiply\:both\:sides\:by\:}10\\\\49\cdot \:10+6.7t\cdot \:10<95.9\cdot \:10\\\\490+67t<959\\\\\mathrm{Subtract\:}490\mathrm{\:from\:both\:sides}\\\\490+67t-490<959-490\\\\simplify\\\\67t<469\\\\\mathrm{Divide\:both\:sides\:by\:}67\\\\\frac{67t}{67}<\frac{469}{67}\\\\t<7[/tex]

Thus the possible amounts of time for which they could rent the meeting room is less than 7

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