Question

1. emmerson has $120. each week, he saves an additional $15. write a function f(x) that models the total amount of money emmerson has after x weeks. (show your work)

f(x) =

1. simplify and solve for x. (show your work)

5(x + 20) = 7x + 30

Explanation:

Problem 11

Step1: Identify initial and weekly amount

Initial amount: $120, Weekly savings: $15, Weeks: \( x \)
Total savings after \( x \) weeks: \( 15x \)

Step2: Form the function

Total amount \( f(x) \) = Initial + Weekly savings
\( f(x) = 15x + 120 \)

Step1: Expand left side

\( 5(x + 20) = 5x + 100 \)

Step2: Subtract \( 5x \) from both sides

\( 5x + 100 - 5x = 7x + 30 - 5x \)
\( 100 = 2x + 30 \)

Step3: Subtract 30 from both sides

\( 100 - 30 = 2x + 30 - 30 \)
\( 70 = 2x \)

Step4: Divide by 2

\( x = \frac{70}{2} = 35 \)

Answer:

\( f(x) = 15x + 120 \)

Problem 12