Question 1147059
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You don't make it clear what you are supposed to do.  If indeed all you are asked to do is write an equation representing the given situation, then you are finished when you write<br>
8x+12y = 120<br>
If you need to find A solution, then you can do some trial and error.  Or you can do what you did and find that two easily identified solutions are (x,y) = (15,0) and (x,y) = (0,10).<br>
The most interesting problem would to be to find ALL the solutions.  In the context of the problem, that means finding all the solutions in non-negative integers.<br>
A standard way to do that is to solve the equation for one variable in terms of the other and use the requirement that the solutions have to be integers to find the solutions.<br>
You can solve for either variable; in this problem I think it will be easier to solve for y.<br>
{{{8x+12y = 120}}}
{{{12y = 120-8x}}}
{{{y = 10 - (2/3)x}}}<br>
Given this form of the equation, and knowing y has to be an integer, we can conclude that (2/3)x must be an integer; and that means x must be a multiple of 3.  Then remembering that both x and y must be non-negative, we can find all the solutions:<br><pre>
   x   y=10-(2/3)x   (x,y)
  -------------------------
   0         10      (0,10)
   3   10-2 = 8      (3,8)
   6   10-4 = 6      (6,6)
   9   10-6 = 4      (9,4)
  12   10-8 = 2      (12,2)
  15  10-10 = 0      (15,0)</pre><br>