To find the value of [tex]\( x \)[/tex], which represents the number of thirty-minute sessions Carly conducted, follow these steps:
1. Set up the equations based on the given information.
- Carly charges \[tex]$15 for each thirty-minute session.
- Carly charges \$[/tex]25 for each sixty-minute session.
- Her total earnings for the weekend were \$230.
- She conducted [tex]\( x \)[/tex] thirty-minute sessions.
- She conducted [tex]\( x - 2 \)[/tex] sixty-minute sessions.
2. Create an equation to represent her total earnings:
- Earnings from thirty-minute sessions: [tex]\( 15x \)[/tex]
- Earnings from sixty-minute sessions: [tex]\( 25(x - 2) \)[/tex]
- Total earnings: [tex]\( 15x + 25(x - 2) = 230 \)[/tex]
3. Simplify the equation:
[tex]\[
15x + 25(x - 2) = 230
\][/tex]
Expand and simplify:
[tex]\[
15x + 25x - 50 = 230
\][/tex]
Combine like terms:
[tex]\[
40x - 50 = 230
\][/tex]
4. Isolate [tex]\( x \)[/tex]:
[tex]\[
40x - 50 = 230
\][/tex]
Add 50 to both sides:
[tex]\[
40x = 280
\][/tex]
Divide both sides by 40:
[tex]\[
x = 7
\][/tex]
Hence, [tex]\( x \)[/tex] is 7. Carly conducted 7 thirty-minute sessions.
The correct answer is:
A. 7
