Question

three pizzas and four sandwiches cost \\$69. three pizzas and seven sandwiches cost \\$87. how much does a sandwich cost?

\\$15
\\$6
\\$9
\\$12

Explanation:

Define variables and translate the problem

Using the Modeling Word Problems knowledge point
Let \(p\) represent the cost of one pizza in dollars.
Let \(s\) represent the cost of one sandwich in dollars.

We translate the given statements into a system of linear equations:

1. "Three pizzas and four sandwiches cost \$69":

$$3p + 4s = 69$$

1. "Three pizzas and seven sandwiches cost \$87":

$$3p + 7s = 87$$

Solve the system of equations

Using the Elimination Method knowledge point
Subtract the first equation from the second equation to eliminate \(p\):

$$(3p + 7s) - (3p + 4s) = 87 - 69$$

$$3s = 18$$

$$s = 6$$

The cost of one sandwich is \$6.

Answer:

• (A) $15
• (B) $6 (Correct answer)
• (C) $9
• (D) $12