How do I solve this equation?

Question

Kumar earns$7.00 per hour. If he works an average of 40 hours a week, what does he earn a week? How much does he earn in a year if he works 50 weeks? One week he worked 10 hours of overtime, for which he earned time-and-a-half pay. What were his total earnings that week?

Answer 1

Hi Arianna! Let's do this question one part at a time.

1. What does he earn in a week? Well, we know he earns $7 per hour, and he works an average of 40 hours per week. We can find what he earns per week by multiplying 7 and 40 to get the following: $7 * 40 = $280 per week.
2. What does he earn in a year? Now we know that he makes $280 per week. If he's working 50 weeks in a year, then we can apply the same concept as in part one to find this answer: $280 * 50 = $14,000 per year.
3. What does he earn with 10 hours of overtime for which he's paid time and a half? What time and a half means is that you take your base rate and multiply it by a factor of 1.5, so in this case you get $7 * 1.5 = $10.50, which gives you his overtime rate. (You can also find this number but cutting 7 in half (3.5) and adding it to 7, which also gives you 10.5.) So, for 10 hours of overtime, he gets $10.50 * 10 = $105 for 10 hours of overtime but the question asks for total earnings. So we add $105 to $280 from the first part and get $385 total for week with 10 hours overtime.

Answer 2

Kumar's rate is $7/hour for a 40 hour work week so in a week he earns

$7/hour * 40 hours/week

$280/week

If the year worked includes the 10 hour of overtime

Then

50 - 1 = 49 weeks Regular pay rate

1 week = 40 hours at Regular pay rate + 10 hours at 1.5(Regular Pay)

Looks like we have

49 weeks * 40 hours/week * $7/hour

(1 week * 40 hours/week * $7/hour)

+ (10 hours * (1.5($7)/hour))

Give it a try.

There are several ways to calculate the annual income for example

50 weeks * $280/week for the regular pay

10 hours * 1.5*$7/hour for the overtime

Either approach should give the same answer.