Question

Company A offers you to pay $\$1100$ as a basic pay a week and pays $\$60$ per hour. The offer made by Company B is given by the graph below. Company C offers you $\$400$ more basic pay as compared to Company A and its hourly rate of pay is half of that of company B. Which company’s offer would you like to accept if all three companies expect you to work for $40$ hours a week?
Assume you will choose the company which is paying you the highest salary for a week.

• A. Either Company A or B
• B. Company A
• C. Company B
• D. Company C

Answer 1

The correct option is C Company B

Detailed step-by-step solution:
Finding the equation of company A:
Let the equation be $y=mx+b,$ where $x$ represents the working time (in hr) and y represents the earning amount $\left(\$\right).$
y-intercept is the value of y when $x=0.$
Basic pay $=\$1100$ (basic pay is the pay when no hours of work is done)
I.e., at $x=0,y=\$1100.$
$\Rightarrow$ y-intercept, $b=1100$
Unit rate $=$ Slope $\left(m\right)=\$60$ per hour
The equation will be $y=60x+1100.$
Total earning from Company A in a week:
Total earnings from Company A in a week will be the value of $y$ when $x=40$ (total working hours in a week).
$\Rightarrow y=60\left(40\right)+1100$
$\Rightarrow y=2400+1100$
$\Rightarrow y=3500$
Total earning from Company A in a week $=\$3500$
Finding the equation of Company B:
Since the line passes through the origin, the line is in the form $y=mx.$
From the graph, consider two points $(0,0)$ and $(20,1800)$.
$\text{Slope}=\frac{\text{Rise}}{\text{Run}}$
$=\frac{\text{Change in y}}{\text{Change in y}}$
$=\frac{1800-0}{20-0}$
$=\frac{1800}{20}$
$=90$
The equation will be $y=90x.$
Total earning from Company B in a week:
Total earning from Company B in a week will be the value of $y$ when $x=40$ (total working hours in a week).
$\Rightarrow y=90\left(40\right)$
$\Rightarrow y=3600$
Total earning from company B in a week $=\$3600.$
Finding the equation of Company C:
Let the equation be $y=mx+b,$ where $x$ represents the working time (in hr) and $y$ represents the earning amount $\left(\$\right).$
Basic pay from company C = $400 + (Basic pay from company A)
$=\$400+\$1100=\$1500$
I.e., at $x=0,y=\$1500.$
y-intercept is the value of $y$ when $x=0.$
$\Rightarrow$ y-intercept, $b=1500$
Hourly rate of pay from Company $C=\frac{1}{2}$ (Hourly rate of pay from Company B)
Slope of the equation of Company $C\left(m\right)=\frac{1}{2}$ (Slope of the equation of Company B)
$=\frac{1}{2}\times 90=45$
The equation will be $y=45x+1500.$
Total earnings from Company C in a week:
Total earning from Company C in a week will be the value of $y$ when $x=40$ (total working hours in a week)
$\Rightarrow y=45\left(40\right)+1500$
$\Rightarrow y=1800+1500$
$\Rightarrow y=3300$
Total earnings from Company C in a week $=\$3300$
Out of the three companies, earnings from Company B is highest, i.e., $\$3600$ in a week.
Hence, Company B’s offer is the best.
$\Rightarrow$ Option B is correct.