Question

A restaurant manager wants to purchase 200 sets of dishes. One design costs $25 per set while

another costs $45 per set. If she only has $ 7400 to spend, how many of each design should she order?
Write a system of linear equations & solve.

Answer 1

To solve this problem, set up a system of linear equations and solve for the values of x and y. The restaurant manager should order 80 sets of the first design dishes and 120 sets of the second design dishes.

Step-by-step explanation:

To solve this problem, we can set up a system of linear equations. Let x represent the number of sets of dishes of the first design, and let y represent the number of sets of dishes of the second design.

From the problem, we know that the total cost of the first design dishes is $25 per set and the total cost of the second design dishes is $45 per set. The total cost of all the sets should not exceed $7400. So, we can write two equations:

1. x+y=200 (equation 1)
2. 25x+45y=7400 (equation 2)

Now, we can solve this system of equations to find the values of x and y. We can use substitution or elimination method.

Let's use the elimination method in this case. We will multiply equation 1 by 25, and equation 2 by -1 to eliminate x:

1. 25x+25y=5000 (equation 3)
2. -25x-45y=-7400 (equation 4)

Adding equations 3 and 4, we get:

-20y=-2400

y=120

Substituting the value of y back into equation 1, we get:

x+120=200

x=80

Therefore, the restaurant manager should order 80 sets of the first design dishes and 120 sets of the second design dishes.

Answer 2

80 sets costing $25/set

120 sets costing $45/set

Step-by-step explanation:

let x = number of sets costing $25/set

let y = number of sets costing $45/set

we have to build eqautions form the info given

(1) . total sets = 200 x + y =200

(2) . total sets = 7400 25x + 45y = 7400

use the substitution method

(rest of work shown below in the picture)