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.
