MHB Solving for X When it Appears Twice

[Dowarner]

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!

 

[Greg]

Hi Dowarner and welcome to MHB! :D

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

$$ax+1.5bx=c$$

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

$$x=\frac{c}{a+1.5b}$$