a restaurant manager wants to purchase 200 sets of dishes. one design costs $25 per set, while another costs…

a restaurant manager wants to purchase 200 sets of dishes. one design costs $25 per set, while another costs $55 per set. if she wants to use her entire budget of $7400, how many of each design should be ordered? she should buy of the $25 sets. she should buy of the $55 sets. (type whole numbers.)

a restaurant manager wants to purchase 200 sets of dishes. one design costs $25 per set, while another costs $55 per set. if she wants to use her entire budget of $7400, how many of each design should be ordered? she should buy of the $25 sets. she should buy of the $55 sets. (type whole numbers.)

Answer

Explanation:

Step1: Set up equations

Let $x$ be the number of $25 - dollar$ sets and $y$ be the number of $55 - dollar$ sets. We have two equations: $x + y=200$ (total number of sets) and $25x + 55y=7400$ (total cost). From $x + y=200$, we get $x = 200 - y$.

Step2: Substitute into cost - equation

Substitute $x = 200 - y$ into $25x+55y = 7400$. So $25(200 - y)+55y=7400$. Expand: $5000-25y + 55y=7400$. Combine like - terms: $30y=7400 - 5000$.

Step3: Solve for $y$

$30y=2400$, then $y=\frac{2400}{30}=80$.

Step4: Solve for $x$

Since $x = 200 - y$, substitute $y = 80$ into it. So $x=200 - 80 = 120$.

Answer:

She should buy 120 of the $25 sets. She should buy 80 of the $55 sets.