Zfarris96idn
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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]$\[tex]$ 25$[/tex][/tex] for each sixty-minute session.

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

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

Sagot :

GinnyAnsweridn
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
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