Question 20 (1 point)

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Susan is offered one job making $30,000 and a raise of $5,000 per year. A different company offers her $40,000 and a raise of $3,000 per year. How long will it take Susan to make more money if she takes the first job?

Question 20 options:

3

4

6

5

shw me hw too so I can put it in my notebok

Answer 1

To determine how long it will take Susan to earn more money with the first job compared to the second job, we can set up an equation based on the total earnings over the years.

1. Define the earnings for each job over time:

   • For the first job:

     • Initial salary: $30,000
     • Annual raise: $5,000
     • Total earnings after \( n \) years = \( 30,000 + 5,000n \)

   • For the second job:

     • Initial salary: $40,000
     • Annual raise: $3,000
     • Total earnings after \( n \) years = \( 40,000 + 3,000n \)

2. Set the earnings from both jobs equal to each other: \[ 30,000 + 5,000n = 40,000 + 3,000n \]

3. Solve for \( n \):

   • First, simplify the equation: \[ 5,000n - 3,000n = 40,000 - 30,000 \] \[ 2,000n = 10,000 \]
   • Now, divide both sides by 2,000: \[ n = \frac{10,000}{2,000} = 5 \]

So it will take 5 years for Susan to make more money if she takes the first job.

Summary for Your Notebook:

• First Job:

  • Salary: $30,000
  • Raise: $5,000/year
  • Earnings after \( n \) years: \( 30,000 + 5,000n \)

• Second Job:

  • Salary: $40,000
  • Raise: $3,000/year
  • Earnings after \( n \) years: \( 40,000 + 3,000n \)

• Equation for comparison: \[ 30,000 + 5,000n = 40,000 + 3,000n \]

• Solution:

  • \( n = 5 \) years

Answer: 5