Respuesta :
A
Let x be the number of hour spent in the studio. Since 225 is a fixed price, and they pay 80 dollars per hour, the total cost will be [tex] 225+80x [/tex]. Jenna has 200 dollars, and can raise 350 more dollars, so she can spend any amount between 200 and 200+350=550. That's why the inequality models this problem.
B
To solve the inequality, subtract 225 to all sides:
[tex] 200 - 225 < 225 + 80x < 550 - 225 \iff -25 < 80x < 325 [/tex]
Divide all sides by 8:
[tex] -\dfrac{25}{80} < x < \dfrac{325}{80} [/tex]
A negative value for x doesn't actually make sense, so the solution space is
[tex] 0 < x < \dfrac{325}{80} = 4.0625[/tex]
So, she can rent the studio for up to 4 hours.
C
The price for 6 hours is
[tex] 225+80\cdot 6 = 705 [/tex]
If Jenna raises 350 dollars, she has 550 dollars. So, she needs
[tex] 705-550 = 155 [/tex]
more dollars to rent the studio for 6 hours
