Question 282741
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.