Question

At a restaurant, there are three different appetizers on the menu: loaded nachos, buffalo wings, and cheese sticks. One group buys 2 plates of buffalo wings and 1 plate of cheese sticks, and spends $23 on appetizers. Another group spends $30.75 to buy 3 plates of loaded nachos and a plate of buffalo wings. A third group buys one of each appetizer, spending $22.25 on appetizers. How much does a plate of loaded nachos cost?

A.$6.50

B.$7.50

C.$7.75

D.$8.25

E.$8.50

Answer 1

B. $7.50

Hope this helps you! Have an amazing day :)

Answer 2

Option B is the correct answer.

Explanation:

Let the price per plate of loaded nachos, buffalo wings, and cheese sticks be n, b and c.

One group buys 2 plates of buffalo wings and 1 plate of cheese sticks, and spends $23.

That is

2b + 1c = 23

2b + c = 23 ----------------------eqn 1

Another group spends $30.75 to buy 3 plates of loaded nachos and a plate of buffalo wings

That is

3n + 1b = 30.75

3n + b = 30.75 ----------------------eqn 2

A third group buys one of each appetizer, spending $22.25

That is

n + b + c = 22.25 ---------------------eqn 3

eqn2 - eqn3

2n - c = 8.5 ---------------------eqn 4

eqn 1 + eqn 4

2b+ 2n = 31.5

b + n = 15.75 ---------------------eqn 5

eqn 3 - eqn 5

c = 6.5

Substituting in eqn 4

2n - 6.5 = 8.5

n = 7.5

Substituting in eqn 3

7.5 + b + 6.5 = 22.25

b = 8.25

Price of nachos n = 7.5 $

Option B is the correct answer.