Question

As a restaurant owner there are many decisions that you need to make on a daily basis, such as where to keep inventory levels. You wish to replenish your stock of dishes by purchasing 250 sets for your restaurant. You have two dish design from which to choose. 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?

Answer 1

The algebraic way:
Let
x = number of $45 sets, and
250-x = number of $20 sets

45x+20(250-x)=6800
25x = 6800-5000
x=1800/25=72
Therefore you would buy 72 sets at $45 and (250-72)=178 sets at $20.

Check the answers.


The layman's way (no calculator, no pencil required):

Buy all 250 sets at $20, that leaves $6800-5000=1800 to spare. For every set we change from $20 to $45, we pay an extra $45-20=$25. So we can change $1800/$25=72 sets.
The answer is therefore 72 sets at $45 and 250-72=178 sets at $20.

Answer 2

7x4