In the expression [tex]2(10x) + 15y[/tex], [tex]x[/tex] represents the number of hours Nina works in a week at her first job, and [tex]y[/tex] represents the number of hours she works in a week at her second job. The expression shows how much money Nina has earned this week. Which statement is true?

A. Nina has worked a total of [tex]x - y[/tex] hours so far this week.
B. Nina works 15 hours a week at her first job.
C. Nina makes [tex]20x[/tex] dollars at her first job each week.
D. Nina makes \$10 per hour at her second job each week.



Answer :

To analyze the expression [tex]\(2(10x) + 15y\)[/tex] and determine which statement is true, let's break down what the expression represents and compare it to each possible statement.

1. Expression Analysis:
The expression given is [tex]\(2(10x) + 15y\)[/tex]. Simplify this expression:
[tex]\[ 2(10x) + 15y = 20x + 15y \][/tex]
This represents the total money Nina earns in a week from both jobs, where:
- [tex]\(x\)[/tex] is the number of hours worked at the first job.
- [tex]\(y\)[/tex] is the number of hours worked at the second job.

2. Statement 1:
"Nina has worked a total of [tex]\(x-y\)[/tex] hours so far this week."

Total hours worked should be [tex]\(x + y\)[/tex] if you add up the hours at both jobs. The term [tex]\(x - y\)[/tex] does not correctly describe the total hours worked. Therefore, Statement 1 is false.

3. Statement 2:
"Nina works 15 hours a week at her first job."

The variable [tex]\(x\)[/tex] represents the hours at her first job, and nothing in the expression or problem implies that [tex]\(x = 15\)[/tex]. Therefore, Statement 2 is false.

4. Statement 3:
"Nina makes [tex]\(20x\)[/tex] dollars at her first job each week."

Looking at the simplified expression [tex]\(20x + 15y\)[/tex], the term [tex]\(20x\)[/tex] comes from [tex]\(2(10x)\)[/tex], which represents Nina’s earnings from the first job. Therefore, Statement 3 is true, as [tex]\(20x\)[/tex] accurately represents her weekly earnings from the first job.

5. Statement 4:
"Nina makes [tex]$10 per hour at her second job each week." In the context of the earnings expression \(20x + 15y\), the coefficient 15 in front of \(y\) suggests that Nina makes $[/tex]15 per hour at her second job, not $10. Therefore, Statement 4 is false.

With all these analyses, the statement that holds true is:

Nina makes [tex]\(20x\)[/tex] dollars at her first job each week.