Question

Working for 4 hours a day, a typist earns $$\$ 65.40$$ a day after taxes. At the same rate of pay, what would he earn per day if he worked for 7 hours a day? (Let \(N\) represent after-tax earnings.) A. \(N=\frac{4}{7}(65.40)\) B. \(N=\frac{7}{4}(65.40)\) C. \(N=4(65.40)\) D. \(N=7(65.40)\)

Short answer

B. \(N=\frac{7}{4}(65.40)\)

Step-by-step solution

Find the typist's hourly rate

The typist earns $65.40 a day after working for 4 hours. To find the typist's hourly rate, divide their daily earnings by the number of hours worked: Hourly rate = \(\frac{Total \ earning}{Hours \ worked}\) \[Hourly \ rate = \frac{65.40}{4}\]

Calculate the typist's earnings for 7 hours

Now, multiply the hourly rate by the new number of hours worked (7 hours) to find the typist's new daily earnings: \(N = Hourly \ rate \times Hours \ worked\) \[N = \frac{65.40}{4} \times 7\]

Simplify the expression

Simplify the expression by multiplying 7 with the top value in the fraction and 4 with the bottom value in the fraction: \[N = \frac{7 \times 65.40}{4}\] Now, we can rewrite this expression as: \[N = \frac{7}{4}(65.40)\] So, the answer is B. \(N=\frac{7}{4}(65.40)\).