As a restaurant owner there are many decisions that you need to make on a daily basis, such as inventory levels. You wish to replenish your stock of dishes by purchasing 250 sets for your restaurant. You have available two different dish designs. One design costs $20 per set and the other $45 per set. If you only have $6,800 to spend, how many of each design should you order? Hint: Let x = the number of $20 dishes and y = the number of $45 dishes.
x + y = 250
and
20x + 45y = 6800
I would change the first to y = 250-x
then sub that into the second,
easy from there ....
To solve this problem, we can set up a system of equations based on the given information.
Let x represent the number of $20 dishes and y represent the number of $45 dishes.
We know that the total number of sets of dishes we want to purchase is 250. This can be expressed as an equation:
x + y = 250 ----(Equation 1)
We also know that the total cost of all the dishes combined should be $6,800. Since each $20 set costs $20 and each $45 set costs $45, we can create another equation for the total cost:
20x + 45y = 6,800 ----(Equation 2)
Now we have a system of two equations that we can solve simultaneously to find the values of x and y.
To solve this system of equations, we can use substitution or elimination method. Let's use the elimination method in this case.
Multiply Equation 1 by 20 to make the coefficients of x in both equations the same:
20x + 20y = 5,000 ----(Equation 3)
Now we can subtract Equation 3 from Equation 2 to eliminate x:
(20x + 45y) - (20x + 20y) = 6,800 - 5,000
25y = 1,800
Dividing both sides of the equation by 25, we get:
y = 72
Now substitute the value of y into Equation 1 to find the value of x:
x + 72 = 250
x = 250 - 72
x = 178
Therefore, you should order 178 sets of the $20 dish design and 72 sets of the $45 dish design to stay within your budget and meet your requirement of 250 sets of dishes.