Answered

Solve your doubts and expand your knowledge with IDNLearn.com's extensive Q&A database. Ask your questions and receive accurate, in-depth answers from our knowledgeable community members.

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

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

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

Sagot :

GinnyAnsweridn
Sure, let's determine the value of [tex]\( x \)[/tex] step by step:

1. Identify the earnings for each session:
- Carly earns \[tex]$15 for each 30-minute session. - Carly earns \$[/tex]25 for each 60-minute session.

2. Set up the total earnings equation:
- Let [tex]\( x \)[/tex] be the number of 30-minute sessions Carly had.
- Thus, she had [tex]\( x - 2 \)[/tex] 60-minute sessions.

3. Formulate the earnings equation:
- The earnings from [tex]\( x \)[/tex] 30-minute sessions: [tex]\( 15x \)[/tex] dollars.
- The earnings from [tex]\( x - 2 \)[/tex] 60-minute sessions: [tex]\( 25(x-2) \)[/tex] dollars.
- The total earnings are given as \$230.

4. Set up the equation:
- The total amount Carly earned can be represented as:
[tex]\[ 15x + 25(x - 2) = 230 \][/tex]

5. Simplify and solve for [tex]\( x \)[/tex]:
- Expand the equation:
[tex]\[ 15x + 25x - 50 = 230 \][/tex]
- Combine like terms:
[tex]\[ 40x - 50 = 230 \][/tex]
- Add 50 to both sides:
[tex]\[ 40x = 280 \][/tex]
- Divide both sides by 40:
[tex]\[ x = 7 \][/tex]

Therefore, the value of [tex]\( x \)[/tex] is:

[tex]\[ \boxed{7} \][/tex]
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to assisting you again.