Question

1. Shamya is passing out newspapers for a summer job. For every paper job, she charges an initial fee plus $6 for each hour of work. Her total fee for a 4-hour job, for instance, $36. Let F(t), denote Shamya's fee for a single job, F(measured in dollars), as a function of the number of hours, t, it took her to complete it. Which formula represents this function? a. F(t) = 60 b. F(t) = 6t+ (36-24) c. F(t) = 6t + 366-0 d. F(t) = 6 + 4(36-6) 36 OA ОС OD 1 N 3

Answer 1

Let's first list down what is given in the scenario to be able to generate the equation.

a.) For every paper job, she charges an initial fee plus $6 for each hour of work.

b.) Her total fee for a 4-hour job is $36.

Step 1: Let's establish variables to represents each value.

F(t) = Shamya's fee for a single job. Measured in dollars.

t = number of hours she worked.

k = initial fee that she charges for every paper job.

Step 2: Let's generate the equation.

Shamya's fee is equal to her initial fee plus $6 multiplied by the number of hours she worked.

We get,

`\text{ F(t) = 6t + k}`

Step 3: Let's determine the value of k = initial fee.

Let's use Shamya's example fee for a 4 - hour job.

At a total fee of $36 for a 4-hour job,

`\text{ F(t) = 6t + k }\rightarrow\text{ 36 = 6(4) + k }\rightarrow\text{ 36 = 24 + k}`
`\text{ k = 36 - 24 }\rightarrow\text{ k = \$12}`

Therefore, the initial fee is $12.

Step 4: Let's complete the equation. Substitute k = $12 or 36 - 24.

`\text{ F(t) = 6t + }12\text{ or F(t) = 6t + (}36\text{ -24)}`

The answer will be letter B.