To solve this problem, we need to find the number of thirty-minute sessions Carly held, denoted as [tex]\( x \)[/tex].
Let's break down the information given:
- Each thirty-minute session earns Carly \[tex]$15.
- Each sixty-minute session earns Carly \$[/tex]25.
- Carly earned a total of \[tex]$230 over the weekend.
- Carly held \( x \) thirty-minute sessions.
- Carly held \( x-2 \) sixty-minute sessions.
We can set up an equation based on this information. The total earnings from the thirty-minute sessions and sixty-minute sessions must equal \$[/tex]230.
First, we'll write an expression for Carly's total earnings from both types of sessions:
- Earnings from thirty-minute sessions: [tex]\( 15x \)[/tex].
- Earnings from sixty-minute sessions: [tex]\( 25(x - 2) \)[/tex].
The total earnings equation is then:
[tex]\[ 15x + 25(x - 2) = 230 \][/tex]
Next, we will simplify and solve this equation:
[tex]\[ 15x + 25(x - 2) = 230 \][/tex]
Distribute the 25 through the term [tex]\( (x - 2) \)[/tex]:
[tex]\[ 15x + 25x - 50 = 230 \][/tex]
Combine like terms:
[tex]\[ 40x - 50 = 230 \][/tex]
Add 50 to both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[ 40x = 280 \][/tex]
Divide both sides by 40 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = 7 \][/tex]
So, the value of [tex]\( x \)[/tex] is 7.
Thus, Carly held 7 thirty-minute sessions.
The correct answer is:
A. 7
