Question

Write and solve a system of equations to answer the question. Check your solution.

At a food court, Pedro and his friends buy 3 pretzels and 2 drinks for a total cost of $5.97. They return
to the same food court and buy 12 more pretzels and 6 more drinks for a total cost of $20.88.
What is the cost of 1 pretzel, and what is the cost of 1 drink?

Answer 1

Answer: Let the cost of one pretzel be $p and the cost of one drink be $d. We can create a system of two equations based on the given information:

3p + 2d = 5.97 (equation 1)

12p + 6d = 20.88 (equation 2)

To solve this system, we can use the elimination method. First, we can multiply equation 1 by 3 to eliminate p:

9p + 6d = 17.91 (equation 3)

Next, we can subtract equation 3 from equation 2 to eliminate p:

3p = 2.97

p = 0.99

Now we can substitute p = 0.99 into equation 1 or equation 2 to solve for d. Let's use equation 1:

3(0.99) + 2d = 5.97

2d = 2.97

d = 1.485

Therefore, the cost of one pretzel is $0.99 and the cost of one drink is $1.485. To check our solution, we can substitute these values into equation 2:

12(0.99) + 6(1.485) = 20.88

This is true, so our solution is correct.

Step-by-step explanation: :)