Q. 63 - Precalculus Enhanced with Graphing Utilities

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 be ordered?

Step-by-Step Solution

Answer

It is necessary to order 80 sets of $25 and 120 sets of $45

Step 1: Given information

A restaurant manager wants to purchase 200 sets of dishes. One design costs $25 per set, while another costs $45 per set 

Step 2: Write and solve the equations

Let x be first design of 25 and y be the another design of 45

there are 200 set of dishes

$x+y=200 \left(1\right)$

She can spent $7400 

Hence $25x+45y=7400 \left(2\right)$

Now multiply equation 1 by 25 and subtract from equation 2

We get,

$25x+25y=5000$

Also

$25x+45y=7400-25x-25y=500020y=2400$

Hence $y=120$

Also

$$\begin{gathered} x+y=200 \\ x=200-120 \\ x=80 \end{gathered}$$

Step 3: Conclusion

It is necessary to order 80 sets of $25 and 120 sets of $45