A man earns $200 for his first 40 hours and is paid one-and-one-half times his rate for overtime. How many hours must he work to earn $230?

A man earns $200 for his first 40 hours and is paid one-and-one-half times his rate for overtime. How many hours must he work to earn $230?

• A. 43
• B. 44
• C. 45
• D. 46

Answer: (B)

To determine how many hours the man needs to work to earn $230, we first need to understand his pay structure. He earns $200 for the first 40 hours, which establishes his hourly wage. To find his hourly rate, we divide his total earnings for these hours by the number of hours worked: \[ \text{Hourly rate} = \frac{200}{40} = 5 \] This means he earns $5 per hour for the first 40 hours. For overtime, he is paid one-and-one-half times his hourly rate, which is: \[ \text{Overtime rate} = 1.5 \times 5 = 7.5 \] Now, let's break down how to reach the target of $230. If he works only the standard 40 hours, he earns $200. To meet the $230 target, he needs an additional: \[ 230 - 200 = 30 \] The extra $30 must be earned through overtime. To find out how many hours are required to earn this extra $30 at the overtime rate of $7.50 per hour, we calculate: \[ \text{Overtime hours needed} = \frac

To determine how many hours the man needs to work to earn $230, we first need to understand his pay structure. He earns $200 for the first 40 hours, which establishes his hourly wage.

To find his hourly rate, we divide his total earnings for these hours by the number of hours worked:

[

\text{Hourly rate} = \frac{200}{40} = 5

]

This means he earns $5 per hour for the first 40 hours. For overtime, he is paid one-and-one-half times his hourly rate, which is:

[

\text{Overtime rate} = 1.5 \times 5 = 7.5

]

Now, let's break down how to reach the target of $230. If he works only the standard 40 hours, he earns $200. To meet the $230 target, he needs an additional:

[

230 - 200 = 30

]

The extra $30 must be earned through overtime. To find out how many hours are required to earn this extra $30 at the overtime rate of $7.50 per hour, we calculate:

[

\text{Overtime hours needed} = \frac