Question

An engineering company charges $80 per hour for new drawings and $60 per hour for site inspections. The company is contracted for 90 hours of new drawings and 150 hours of site inspections the first week of the month. They had to pay $15,000 in payroll during the same week.

Part A
Which function represents the company's earnings for the week?
A. f(x) = 140x
B. f(x) = 140x – 15,000
C. f(d, s) = 90d + 150s
D. f(d, s) = 80d + 60s
Part B
Did they earn more money than the cost of payroll? Choose the correct explanation.
A. Yes; Since f(90, 150) > 15,000, they did earn more money than the cost of payroll.
B. Yes; Since f(240) > 15,000, they did earn more money than the cost of payroll.
C. No; Since f(90, 150) < 15,000, they did not earn more money than the cost of payroll.
D. No; Since f(80, 60) < 15,000, they did not earn more money than the cost of payroll.

Answer 1

Let's break down the problem step by step.

**Part A**

We're looking for a function that represents the company's earnings for the week based on the hours spent on new drawings and site inspections.

1. The income from new drawings is calculated as:
- $80 per hour for 90 hours: \( 80 \times 90 = 7200 \)

2. The income from site inspections is calculated as:
- $60 per hour for 150 hours: \( 60 \times 150 = 9000 \)

3. Therefore, the total earnings \(E\) from both services is:
\[
E = 7200 + 9000 = 16200
\]

The function that represents the company's earnings can be given in terms of variables \(d\) (new drawings) and \(s\) (site inspections) as follows:
- For each hour of drawings, they earn $80, and for each hour of site inspections, they earn $60. Thus, the function representing the earnings is:
\[
f(d, s) = 80d + 60s
\]

The correct answer is:
**D. f(d, s) = 80d + 60s**

**Part B**

Now, we need to determine if they earned more money than the cost of payroll, which is $15,000.

1. To find the earnings using the function derived above with \(d = 90\) and \(s = 150\):
\[
f(90, 150) = 80 \times 90 + 60 \times 150
\]

Calculating this:
- \(80 \times 90 = 7200\)
- \(60 \times 150 = 9000\)

Adding these together:
\[
f(90, 150) = 7200 + 9000 = 16200
\]

2. Now, we need to compare $16,200 with the payroll cost of $15,000:
\[
16200 > 15000
\]

Thus, they earned more than the cost of payroll.

The correct explanation is:
**A. Yes; Since f(90, 150) > 15,000, they did earn more money than the cost of payroll.**