Select the correct answer.

Carly tutors students in math on the weekends and offers both thirty-minute sessions and sixty-minute sessions. She earns [tex]\$ 15[/tex] for each thirty-minute session and [tex]\$ 25[/tex] for each sixty-minute session.

If she earned [tex]\$ 230[/tex] this past weekend and had [tex]x[/tex] thirty-minute sessions and [tex]x-2[/tex] sixty-minute sessions, what is the value of [tex]x[/tex]?

A. 5
B. 8
C. 6
D. 7



Answer :

To find the value of [tex]\( x \)[/tex] given Carly's tutoring earnings, we can follow these steps:

1. Identify the rates and total earnings:
- Carly earns \[tex]$15 for each thirty-minute session. - Carly earns \$[/tex]25 for each sixty-minute session.
- Her total earnings for the weekend were \$230.

2. Translate the problem into an equation:
- Let [tex]\( x \)[/tex] be the number of thirty-minute sessions.
- Since she had [tex]\( x - 2 \)[/tex] sixty-minute sessions, the income from these sessions is [tex]\( 25(x - 2) \)[/tex].

3. Set up the equation for the total earnings:
- Total earnings from thirty-minute sessions: [tex]\( 15x \)[/tex]
- Total earnings from sixty-minute sessions: [tex]\( 25(x - 2) \)[/tex]
- Combined total earnings: [tex]\( 15x + 25(x - 2) = 230 \)[/tex]

4. Simplify and solve the equation:
[tex]\[ 15x + 25(x - 2) = 230 \][/tex]
[tex]\[ 15x + 25x - 50 = 230 \][/tex]
[tex]\[ 40x - 50 = 230 \][/tex]
[tex]\[ 40x = 230 + 50 \][/tex]
[tex]\[ 40x = 280 \][/tex]
[tex]\[ x = 7 \][/tex]

Therefore, the value of [tex]\( x \)[/tex] is [tex]\( \boxed{7} \)[/tex].

So, the correct answer is:
D. [tex]\( 7 \)[/tex]