solve an equation with two variables ie: 32800 = 320n +340z

Question

A nursing home has two daily rates, 320 for a semi room & 340 for a private room.  Total revenue is 32,800.

How many days are there each for semi and private rooms.  (Answer is 60 semi & 40 private days)  How do you solve this equation and is it written correctly?

Answer 1

x = number of semi rooms

y = number of private rooms

The equation for this problem would be:

320x + 340y = 32800

Because this is a single equation in 2 variables, there is more than one correct answer.  For there to be only one correct answer, there needs to be more information so that I could set up a second equation.

To check the provided answer, I am going to substitute the numbers that I was given into the equation that I found.

320(60) + 340(40) = 32,800

19,200 + 13,600 = 32,800

32,800 = 32,800

The answer 60 semi and 40 private is a solution, but it is not the only possible solution for this problem.
 (I have not taken the time to see if this is the only solution that gives whole numbers for both x and y.)