Question 316258
I think you might have double posted this question, it's OK, I hope this is helpful. 

x=the number of $20 dishes 
y=the number of $45 dishes 

Since you want to purchase 250 total, {{{x + y = 250}}}. We can rewrite this as {{{y = 250 - x }}}. (eq1) 

Now suppose you buy 4 of the $20 dishes and 2 of the $45 dishes. The you spend 4*$20 = $80 on the four $20 dishes and 2*$45= $90 on the two $45 dollar dishes. 

In general, you multiply. So if you buy x dishes for $20, you spend 20*x dollars on them. Then if you buy y dishes for $45, you spend 45*y on them. The total amount of money you spend is {{{20x + 45y}}}, and since we know that you have $6800, we get {{{ 20x + 45y = 6800 }}}. (eq2) 

Let us substitute our equation for y given by (eq1) into (eq2). 

{{{ 20x + 45y = 20x + 45(250-x) = 6800 }}} 

{{{20x + 45(250-x) = 6800 }}} 

Distributing the 45 gives 

{{{20x + 11250 -45x = 6800 }}} 

Combining like terms gives 

{{{-25 x + 11250 = 6800}}}

Add 25x to both sides to get 

{{{ 11250 = 6800 + 25x }}} 

Subtract 6800 from both sides to get 

{{{4450 = 25x }}} 

Divide both sides by 25 to get 

{{{ 178 = x }}} 

Thus, from (eq1) we can get {{{y = 250 - x = 250 - 178 = 72}}}. So you should buy 178 of the $20 dish sets and you should buy 72 of the $45 dish sets. 

Now let us check. The total number of dish sets you buy is 178 + 72 which is a total of 250 as you requested. The amount of money you pay is a total of 178 * $20 = $ 3560 for the $20 dishes and 72 * $45 = $3240 for the $45 dishes. This means you spend #3560 + $3240 = $6800. 

Good luck on the restaurant business! 

Take care, 
Mo