Questions: Ethan received 1,500 bonus to start his new job after graduating college. He also makes 4,000 per month. Write a linear function in slope-intercept form to represent his total amount of money based on the number of months worked. THEN determine how much money he will have after 6 months. Be sure to define variables and use proper labels. SHOW ALL WORK!

Ethan received 1,500 bonus to start his new job after graduating college. He also makes 4,000 per month. Write a linear function in slope-intercept form to represent his total amount of money based on the number of months worked. THEN determine how much money he will have after 6 months. Be sure to define variables and use proper labels. SHOW ALL WORK!
Transcript text: Ethan received $1,500 bonus to start his new job after graduating college. He also makes $4,000 per month. Write a linear function in slope-intercept form to represent his total amount of money based on the number of months worked. THEN determine how much money he will have after 6 months. Be sure to define variables and use proper labels. SHOW ALL WORK!
failed

Solution

failed
failed

Solution Steps

To solve this problem, we need to create a linear function that represents Ethan's total amount of money based on the number of months worked. The linear function will be in the form \( y = mx + b \), where \( m \) is the monthly income and \( b \) is the initial bonus. After defining the function, we will calculate the total amount of money Ethan will have after 6 months.

Solution Approach
  1. Define the variables:
    • \( y \): Total amount of money
    • \( x \): Number of months worked
    • \( m \): Monthly income (\$4,000)
    • \( b \): Initial bonus (\$1,500)
  2. Write the linear function in slope-intercept form: \( y = mx + b \)
  3. Substitute \( x = 6 \) into the function to find the total amount of money after 6 months.
Step 1: Define the Variables

Let \( y \) represent the total amount of money Ethan has after working \( x \) months. The monthly income is \( m = 4000 \) and the initial bonus is \( b = 1500 \).

Step 2: Write the Linear Function

The linear function representing Ethan's total amount of money based on the number of months worked is given by: \[ y = mx + b \] Substituting the values of \( m \) and \( b \): \[ y = 4000x + 1500 \]

Step 3: Calculate Total Money After 6 Months

To find the total amount of money after 6 months, substitute \( x = 6 \) into the linear function: \[ y = 4000(6) + 1500 \] Calculating this gives: \[ y = 24000 + 1500 = 25500 \]

Final Answer

Ethan will have a total of \(\boxed{25500}\) dollars after 6 months.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
How do you ask for someone's last name in Spanish?
failedAnswered
A piece of wire of length 62 is cut, and the resulting two pieces are formed to make a circle and a square. Where should the wire be cut to (a) minimize and (b) maximize the combined area of the circle and the square? (a) To minimize the combined area, the wire should be cut so that 27.274 are used for the circle and 34.726 are used for the square. (Type integers or decimals rounded to the nearest thousandth as needed.) (b) To maximize the combined area, the wire should be cut so that are used for the circle and are used for the square. (Type integers or decimals rounded to the nearest thousandth as needed.)
failedAnswered
Two cars start moving from the same point. One travels south at 20 mi / h and the other travels west at 15 mi / h. At what rate (in mi/h) is the distance between the cars increasing three hours later?
failedAnswered
Given the frequency table below, what is the relative frequency of the data value 1 ? Value Frequency 1 6 2 5 3 5 4 2 5 7
failedAnswered
Classify the statement as an example of classical probability, empirical probability, or subjective probability. The probability that a newborn baby is a boy is 1/2. A. classical probability B. subjective probability C. empirical probability