MHB Solving for X When it Appears Twice

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The algebra problem involves calculating an employee's hourly rate (x) based on a known weekly salary (c) and the hours worked at different rates. The equation provided is (a*x) + (b*1.5x) = c, where a represents regular hours and b represents overtime hours. The solution involves isolating x, resulting in the formula x = c / (a + 1.5b). This allows for the calculation of the hourly rate based on the total hours worked and the salary. The discussion confirms the setup and provides the correct method for solving the equation.
Dowarner
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I've run into my first real life algebra problem and my high school algebra memory isn't cutting it.

Here's the problem:

To fit budget, an employee of a company needs to earn a known weekly salary (c)
The company's boss needs to calculate the employee's regular hourly rate (x) based on the number of hours they work in the week to get to that salary
Hours are worked at two different rates, however. Regular hours (a) are worked at the rate of "x" and overtime hours are worked at "1.5x".

This leaves us with the equation of:
(a*x) + (b*1.5x)=c

I need to isolate for x as a,b and c are all known.

Please help!
 
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Hi Dowarner and welcome to MHB! :D

Your problem appears to be set up correctly. Here's what I have for your request:

$$ax+1.5bx=c$$

$$x(a+1.5b)=c$$

$$x=\frac{c}{a+1.5b}$$
 
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