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Labron makes [tex]$\$[/tex]100[tex]$ per week and takes no vacation during the entire year. His friend, Jordan, makes $[/tex]\[tex]$4800$[/tex] per year at the same weekly rate. Jordan takes [tex]$x$[/tex] vacation weeks per year.
Note: There are 52 weeks in a year.

This equation represents how to find Jordan's number of vacation weeks:
[tex]\[
100(52-x) = 4800
\][/tex]

Labron says that Jordan takes 4 weeks of vacation each year. Is he correct? Check all that apply.

A. Yes, he is correct because substituting [tex]$x=4$[/tex] into the equation yielded a true statement.
B. Yes, he is correct because substituting [tex]$x=4$[/tex] into the equation yielded a false statement.
C. No, he is incorrect because substituting [tex]$x=4$[/tex] into the equation yielded a true statement.
D. No, he is incorrect because substituting [tex]$x=4$[/tex] into the equation yielded a false statement.

Sagot :

GinnyAnswer
Let's find out if Labron's statement is correct by verifying it step-by-step.

1. Set up the problem:

Jordan makes \[tex]$100 per week, and he makes a total of \$[/tex]4800 per year. We need to find out how many weeks, [tex]\( x \)[/tex], Jordan takes as vacation.

2. Use the given equation:

[tex]\[ 100(52 - x) = 4800 \][/tex]

Here,
- [tex]\( 100 \)[/tex] is the weekly rate of pay.
- [tex]\( 52 - x \)[/tex] represents the weeks Jordan works in a year since there are 52 weeks in a year and he takes [tex]\( x \)[/tex] weeks of vacation.
- [tex]\( 4800 \)[/tex] is the total amount Jordan earns in a year.

3. Solve the equation for [tex]\( x \)[/tex]:

Substitute and solve for [tex]\( x \)[/tex]:

[tex]\[ 100(52 - x) = 4800 \][/tex]

Divide both sides by 100 to simplify:

[tex]\[ 52 - x = \frac{4800}{100} \][/tex]

Calculate:

[tex]\[ 52 - x = 48 \][/tex]

Then, isolate [tex]\( x \)[/tex]:

[tex]\[ x = 52 - 48 \][/tex]

[tex]\[ x = 4 \][/tex]

So, we found that [tex]\( x = 4 \)[/tex].

4. Verify Labron's statement:

Labron says Jordan takes 4 weeks of vacation each year. Let's verify by substituting [tex]\( x = 4 \)[/tex] back into the original equation:

[tex]\[ 100(52 - 4) = 4800 \][/tex]

Calculate within the parentheses first:

[tex]\[ 52 - 4 = 48 \][/tex]

Then, multiply:

[tex]\[ 100 \times 48 = 4800 \][/tex]

This is a true statement.

Conclusion:

Labron's statement is correct because substituting [tex]\( x = 4 \)[/tex] into the equation yielded a true statement.

So the correct answer is:

Yes, he is correct because substituting [tex]\( x = 4 \)[/tex] into the equation yielded a true statement.
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