SOLUTION: The amount of money that Pablo makes in a given week varies directly as the number of hours he works that week. In a week in which he works 38 hours, he makes $589. How much will b

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Question 250216: The amount of money that Pablo makes in a given week varies directly as the number of hours he works that week. In a week in which he works 38 hours, he makes $589. How much will be make in a week in which he works 46 hours?
Answer by solver91311(24713) About Me  (Show Source):
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Let represent the weekly paycheck. Let represent the number of hours worked. Let represent the constant of proportionality, or in the limited context of this problem, Pablo's hourly rate of pay. Therefore, in the completely general case of working time units at a rate of monetary units per time unit worked, excluding consideration of overtime bonuses or deduction of taxes, etc., the value of a paycheck is given by:



But we know that in Pablo's case, dollars when hours, so:

dollars per hour.

So, in Pablo's general case:



And in the specific case of working 46 hours:



You can do the arithmetic.

John