Question

At a restaurant, there are three different appetizers on the menu: spring rolls, chicken tenders, and pretzel dippers. One group buys 2 plates of chicken

tenders and 1 plate of pretzel dippers, and spends $23 on appetizers. Another group spends $30.75 to buy 3 plates of spring rolls and a plate of chicken
tenders. A third group buys one of each appetizer, spending $22.25 on appetizers.
How much does a plate of spring rolls cost?
A. $7.75
B. $8.50
C. $7.50
D. $6.50

Answer 1

Answer: A

Step-by-step explanation: To solve this problem, we can set up a system of equations to represent the information given in the problem. Let x represent the cost of a plate of spring rolls, y represent the cost of a plate of chicken tenders, and z represent the cost of a plate of pretzel dippers.

The first group spent $23 on 2 plates of chicken tenders and 1 plate of pretzel dippers, so the equation for this group is:

2y + z = $23

The second group spent $30.75 to buy 3 plates of spring rolls and 1 plate of chicken tenders, so the equation for this group is:

3x + y = $30.75

The third group spent $22.25 on one of each appetizer, so the equation for this group is:

x + y + z = $22.25

Now that we have three equations, we can use algebraic techniques to solve for the value of x, which represents the cost of a plate of spring rolls.

First, we can solve the second equation for y:

y = $30.75 - 3x

Substituting this expression for y into the first equation, we get:

2($30.75 - 3x) + z = $23

Solving for x, we find that x = $7.75.

Therefore, the cost of a plate of spring rolls is $7.75, so the answer is A.