Answer
The manager should buy 120 sets for the \$45 design and 80 sets for the \$25 design.
Work Step by Step
We can represent each number of sets of dishes bought as $x+y=200$ where x is the number of sets of the \$25 dishes and y is the number of sets of the \$45 dishes.
We can represent the cost spent per month as: $25x+45y=7400$
If the manager wants to spend exactly \$7400, we can find out how many sets of each design she should order by isolating one of the variables:
$x=200-y$
$25(200-y)+45y=7400$
$5000-25y+45y=7400$
$20y=7400-5000$
$y=2400/20$
$y=120$ sets of the \$45 design
$x=200-120=80$ sets of the \$25 design.
