Question

Labron makes $100 per week and takes no vacation during the entire year. His friend, Jordan, makes $4800 per year at the same weekly rate. Jordan takes x vacation weeks per year.

 Note: There are 52 weeks in a year.

This equation represents how to find Jordan’s number of vacation weeks.

  100(52 – x) = 4800

Labron says that Jordan takes 4 weeks of vacation each year. Is he correct? Check all that apply.
Yes, he is correct because substituting x = 4 into the equation yielded a true statement.
Yes, he is correct because substituting x = 4 into the equation yielded a false statement.
No, he is incorrect because substituting x = 4 into the equation yielded a true statement.
No, he is incorrect because substituting x = 4 into the equation yielded a false statement.

Answer 1

To determine if Labron's statement about Jordan taking 4 weeks of vacation is correct, we need to substitute \( x = 4 \) into the equation and see if it holds true.

The equation given is:

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

Substituting \( x = 4 \):

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

Calculating inside the parentheses:

\[ 100(48) = 4800 \]

Now calculate:

\[ 4800 = 4800 \]

The statement is true since both sides are equal.

Now, let's review the answer options:

1. **Yes, he is correct because substituting x = 4 into the equation yielded a true statement.** (This is correct.)
2. Yes, he is correct because substituting x = 4 into the equation yielded a false statement. (This is incorrect.)
3. No, he is incorrect because substituting x = 4 into the equation yielded a true statement. (This is incorrect.)
4. No, he is incorrect because substituting x = 4 into the equation yielded a false statement. (This is incorrect.)

Therefore, the correct answer is:

**Yes, he is correct because substituting x = 4 into the equation yielded a true statement.**