Question 282741: A restaurant owner wishes to replenish his stock of dishes by purchasing 250 sets for your restaurant. You have available two different dish designs. One design costs $20 per set (X) and the other $45 per set (Y). If you only have $6,800 to spend, how many of each design should you order? How do I write as linear eqaution and solve
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x = number of sets of dishes that cost $20 per set.
y = number of sets of dishes that cost $45 per set.
Total number of sets of dishes is equal to 250.
Total amount of money you have to spend is equal to $6800.
You have 2 equations that have to be solved simultaneously.
The first equation is the number of sets of dishes and is equal to:
x + y = 250
The second equation is the total money you have to spend on each set of dishes that will add up exactly to $6800 and is equal to:
20*x + 45*y = 6800
You can solve these 2 equations by either substitution or addition method.
We'll use substitution.
Take the first equation and solve for x or y.
we'll solve for x to get x = 250 - y
Substitute this value for x in the second equation to get:
20*x + 45*y = 6800 becomes 20*(250-y) + 45*y = 6800.
Simplify to get:
5000 - 20*y + 45*y = 6800
Simplify further to get:
5000 + 25*y = 6800
Subtract 5000 from both sides of this equation to get:
25*y = 1800
Divide both sides of this equation by 25 to get:
y = 72
Since x + y = 250, then x = 178
You need to buy 178 sets of dishes at $20 per set and 72 sets of dishes at $45 per set in order for you to buy a total of 250 sets of dishes and spend a total of $6800 exactly.
178 * 20 + 72 * 45 = 6800 confirming these values are good.
Your answer is:
You need to purchase 178 sets of dishes at $20 per set, and 72 sets of dishes at $45 per set.
|
|
|
