Julio is paid 1.5 times his hourly rate for each hour he works over 40 hours in a week. Last week he worked 45 hours and earned $641.25. Write and solve an equation to find Julio's normal hourly rate.

Answer 1

Let x represent the hourly rate. For all the hours that Julio works (up to 40 hours) his pay is x times the number of hours. For any time over 40 hours, his pay is 1.5 times x times the number of hours. So for 45 hours, his total pay is (40 times x) + (5 times 1.5 times x). Since it tells us that he made $641.25, you can write the equation as 40x + 5 (1.5x) = 641.25. Multiplying 5 by 1.5, you get 40x + 7.5x = 641.25. Then combine the terms on the left-hand side of the equation to get 47.5x = 641.25. To solve the equation, divide both sides by 47.5 to get x = 13.5.

Answer 2

First, define the variables. Let’s let x = his regular pay.

So when he gets paid his regular amount, to find out how much he gets, we multiply his pay rate and the number of hours he works. For instance, if he makes $10/hr and works 4 hours he gets paid $40. So, since he works up to and including 40 hours for his regular pay rate, we can say that the amount he earned is 40x. But he worked 5 more hours. And for this 5 more hours, he got paid 1.5 times his regular pay rate, so (5)(1.5x). To find his total, we add the two pieces together and we are told it equals $641.25 so:

40x + 5(1.5x) = 641.25

To solve, simplify, combine like-terms, and isolate “x” by dividing. I’ll let you do that part.

Answer 3

I will model this for you with 1.6, 50, 55, 650.

Normal hourly rate is h.

First 50 hours : he earns h per hr, so 50h in total.

Hours after 50 : 55 - 50 = 5.

For these 5 hours he earns 1.6h per hour, so total of 5 x.1.6h

Total earned : 50h + 5 x 1.6h = 50h + 8h = 58h

58h = 650

h = 650 / 58 = $ 11.21 per hour

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Now use my model to figure your problem out. (you should get $ 13.50).

Mike