Tom usually works x hours in a week at $14 per hour. The hourly wages for overtime is 1 1/2 times the normal hourly wages. In a certain week, he worked 54 hours and his total salary was $819. Find the value of x.
In a normal week, Tom's salary would be $14 * x.
For overtime, he worked 54 - x hours.
His overtime salary would be (1 1/2) * $14 * (54 - x).
Adding his normal salary and overtime salary, his total salary was $819.
So, his total salary is equal to $14 * x + (1 1/2) * $14 * (54 - x) = 819.
This simplifies to $14 * x + $21 * (54 - x) = 819.
Expanding the expression further, we get $14 * x + $21 * 54 - $21 * x = 819.
Combining like terms, we get $7 * x + $21 * 54 = 819.
Subtracting $21 * 54 from both sides of the equation, we get $7 * x = 819 - $21 * 54 = 819 - $1134 = -315.
Dividing both sides of the equation by $7, we get x = -315 / 7 = -45.
Thus, the value of x is equal to -45. Answer: \boxed{-45}.
To find the value of x, we can set up an equation based on the given information.
Let's begin by finding the salary for the regular hours worked.
Regular hours worked = x hours
Hourly wage = $14
Regular salary = Regular hours worked * Hourly wage
Next, let's find the salary for the overtime hours worked.
Overtime hours worked = 54 - x hours
Hourly wage for overtime = 1 1/2 * Hourly wage = 1.5 * $14
Overtime salary = Overtime hours worked * Hourly wage for overtime
We know that the total salary is $819, so we can write the equation:
Regular salary + Overtime salary = $819
Substituting the values we found earlier, we get:
x * $14 + (54 - x) * (1.5 * $14) = $819
Simplifying the equation:
14x + (54 - x)(21) = 819
14x + 1134 - 21x = 819
-7x = -315
Dividing both sides by -7:
x = 45
Therefore, the value of x is 45.