Al has secured an internship at a bank. He receives double pay for every hour he works over and above 38 hours per week. Last week, he worked 48 hours and earned £812.
Formulate a linear equation for this scenario in terms of x, for Al's regular hourly wage.
regular hourly wage ---- x
overtime rate ------ 2x
so :
38x + 10(2x) = 812
solve for x to find his regular hourly wage
Thank you, confirmed as same working out and solution as my own after consideration. Thanks for clear working
To formulate a linear equation for this scenario, let's break it down:
Let x be Al's regular hourly wage.
Al works 38 hours per week at this regular hourly rate.
For every hour he works over 38 hours, Al receives double pay.
Therefore, the equation for Al's earnings can be expressed as follows:
Earnings = Regular wage for 38 hours + Double pay for extra hours
Earnings = x * 38 + 2 * x * (extra hours)
Given that Al worked 48 hours, we can subtract the initial 38 hours to find the number of extra hours:
Extra hours = 48 - 38 = 10
Substituting this into the equation, we get:
Earnings = x * 38 + 2 * x * 10
Simplifying further:
Earnings = 38x + 20x
Earnings = 58x
Now we know that Al earned £812, so we can set the equation equal to this value:
812 = 58x
Therefore, the linear equation in terms of x for Al's regular hourly wage is:
58x = 812