SOLUTION: Restaurant owner want to purchase 250 sets of dishes. He has two designs, one $20 & $45. I have $6800 to spend. How many of each designs should I order? Please show step by step

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Restaurant owner want to purchase 250 sets of dishes. He has two designs, one $20 & $45. I have $6800 to spend. How many of each designs should I order? Please show step by step      Log On


   

Question 316441: Restaurant owner want to purchase 250 sets of dishes. He has two designs, one $20 & $45. I have $6800 to spend. How many of each designs should I order? Please show step by step solutions for x & y. x = $20 y = $45 Thanks
Answer by moshiz08(60) About Me  (Show Source):
You can put this solution on YOUR website!
x=the number of $20 dishes
y=the number of $45 dishes
Since you want to purchase 250 total, x+%2B+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+%2B+45y, and since we know that you have $6800, we get +20x+%2B+45y+=+6800+. (eq2)
Let us substitute our equation for y given by (eq1) into (eq2).
+20x+%2B+45y+=+20x+%2B+45%28250-x%29+=+6800+
20x+%2B+45%28250-x%29+=+6800+
Distributing the 45 gives
20x+%2B+11250+-45x+=+6800+
Combining like terms gives
-25+x+%2B+11250+=+6800
Add 25x to both sides to get
+11250+=+6800+%2B+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.