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.
