Zfarris96idn
Answered

Find answers to your most challenging questions with the help of IDNLearn.com's experts. Our experts are available to provide in-depth and trustworthy answers to any questions you may have.

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]$\[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
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. IDNLearn.com has the solutions you’re looking for. Thanks for visiting, and see you next time for more reliable information.