Chapter 11.1, Problem 63AYU

To determine

To find: A restaurant manager wants to purchase 200 sets of dishes. One design costs $25 per set, and another costs $45 per set. If she has only $7400 to spend, how many sets of each design should she order?

Answer to Problem 63AYU

Solution:

One design cost is $80 and another is 120.

Explanation of Solution

Given:

Arestaurant manager wants to purchase 200 sets of dishes. One design costs $25 per set, and another costs $45 per set. She has only $7400 to spend.

Calculation:

Let one design be $x$ and another be $y$ .

  $x+y=200\to -1$

  $25x+45y=7400\dots -2$

Multiplying equation 1 by 25 and subtracting from equation 2 we have,

  $25x+45y=7400$

  $25x+25y=5000$

  $20y=2400$

  $y=120$

Substituting the value of $y$ in equation 1 we have,

  $x+120=200$ ]

  $x=80$

Therefore, one design cost is $80 and another is $120.