SOLUTION: Set up the system of equations needed to solve the following problem. A company produces two types of widgets in two different factories. Factory A produces 25 standard and 50

Question 834512: Set up the system of equations needed to solve the following problem.
A company produces two types of widgets in two different factories. Factory A produces 25 standard and 50 deluxe widgets per day. Factory B produces 150 standard and 75 deluxe widgets per day. How many days should the company operate each factory in order to exactly fill an order for 500 standard and 325 deluxe widgets?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
= number of days factory A needs to work to exactly fill that order.
= number of days factory B needs to work to exactly fill that order.

During days, factory A can make standard widgets.
During days, factory B can make standard widgets.
To make the 500 standard widgets and have to satisfy the equation
.
We can simplify that equation a bit by dividing both sides of the equal sign by 25.

During days, factory A can make deluxe widgets.
During days, factory B can make deluxe widgets.
To make the 325 deluxe widgets and have to satisfy the equation
.
We can simplify that equation a bit by dividing both sides of the equal sign by 25.

We can set up the simpler system

or we could have stopped before simplifying the equations and end up with

IF WE HAD TO SOLVE THE SYSTEM:
There are several ways to solve the system.
We could solve for to get an expression that is equal to ,
--->
and the substitute the expression for in the other equation:
-->
Then we solve the resulting equation for

Then we would substitute the value found for into and get

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