Last week, before taxes, you earned $386 after working 18 hours at your regular hourly rate and 8 hours at time-and-a- half. Create a linear function from this word problem.
Question
Last week, before taxes, you earned $386 after working 18 hours at your regular hourly rate and 8 hours at time-and-a- half. Create a linear function from this word problem.
Solution
Let's denote the regular hourly rate as x. Therefore, the rate for time-and-a-half would be 1.5x.
From the problem, we know that the total earnings for the week before taxes is $386. This total is made up of the earnings from the regular hourly rate and the earnings from the time-and-a-half rate.
The earnings from the regular hourly rate is the rate (x) times the number of hours worked at this rate (18 hours). So, this is 18x.
The earnings from the time-and-a-half rate is the rate (1.5x) times the number of hours worked at this rate (8 hours). So, this is 8*1.5x = 12x.
Therefore, the total earnings for the week is the sum of these two amounts, which gives us the equation:
18x + 12x = $386
This is the linear function that represents the word problem.
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