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

If she earned [tex]\$230[/tex] 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[/tex]?

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


Sagot :

To determine the value of [tex]\( x \)[/tex], we start by interpreting the given information.

Carly earns [tex]\(\$15\)[/tex] for each thirty-minute session and [tex]\(\$25\)[/tex] for each sixty-minute session. The total amount she earned over the past weekend is [tex]\(\$230\)[/tex]. Additionally, she held [tex]\( x \)[/tex] thirty-minute sessions and [tex]\( x-2 \)[/tex] sixty-minute sessions.

Given this information, we can set up an equation based on her earnings from both types of sessions. The equation representing her total earnings is:

[tex]\[ 15x + 25(x - 2) = 230 \][/tex]

First, we distribute the 25 in the second term:

[tex]\[ 15x + 25x - 50 = 230 \][/tex]

Next, we combine like terms:

[tex]\[ 40x - 50 = 230 \][/tex]

Next, we need to isolate [tex]\( x \)[/tex]. Begin by adding 50 to both sides of the equation:

[tex]\[ 40x - 50 + 50 = 230 + 50 \][/tex]

[tex]\[ 40x = 280 \][/tex]

Now, divide both sides of the equation by 40 to solve for [tex]\( x \)[/tex]:

[tex]\[ x = \frac{280}{40} = 7 \][/tex]

So, the value of [tex]\( x \)[/tex] is [tex]\( 7 \)[/tex].

Therefore, the correct answer is
[tex]\[ \boxed{7} \][/tex]