Systems of Equations

Question

A restaurant manager wants to purchase 200 sets of dishes. One design costs ​$15 per​ set, while another costs ​$55 per set. If she wants to use her entire budget of ​$8​200, how many of each design should be​ ordered?

Answer 1

Let x = the number of $15 sets and y = the number of $55 sets

Then we have the following system of equations to solve for x and y.

15x + 55y = 8200 (from the budget of $8200)

x + y = 200 (from the total number of sets)

Substitute 200 – y for x in the first equation to get

15(200 – y) + 55y = 8200

which means that

3000 – 15y + 55y = 3000 + 40y = 8200

Subtract 3000 from both sides to get

40y = 5200

which means that

y = 5200/40

This tells you the number of $55 sets ordered

SInce x = 200 – y

you just need to plug in the value of y you solved for above and you have

x (the number of $15 sets ordered)

Hope this helps. Leave a comment if you have any questions.