Isabella went into a movie theater and bought 3 drinks and 10 pretzels, costing a total of $54.50. Jason went into the same movie theater and bought 9 drinks and 5 pretzels, costing a total of $57.25. Determine the price of each drink and the price of each pretzel.

The cost of 1 drink = $4.1

The cost of 1 pretzel = $4.22

Step-by-step explanation:

Let us assume the cost of 1 drink = $ m

And the cost of 1 pretzel = $ n

Now, the cost of 3 drinks = 3 x (cost of 1 drink) = 3 x ($ m) = 3 m

The cost of 10 pretzels = 10 x (cost of 1 pretzel) = 10 x ($ n) = 10 n

So, the total cost of 3 drinks + 10 pretzels = 3 m + 10 n

Also, Isabella paid $54.50 fro 3 drinks and 10 pretzels.

⇒3 m + 10 n = $54.50 ... (1)

Again, the cost of 9 drinks = 9 x (cost of 1 drink) = 9 x ($ m) = 9 m

The cost of 5 pretzels = 5 x (cost of 1 pretzel) = 5 x ($ n) = 5 n

So, the total cost of 9 drinks + 5 pretzels = 9 m + 5 n

Also, Jason paid $57.25 fro 9 drinks and 5 pretzels.

⇒9 m + 5 n = $57.25 ... (2)

Solving (1) and (2) fro the values of m, n.

Multiply equation (1) with (-3) and add with (2), we get:

9 m + 5 n - 9 m - 30 n = 57. 25 - 162.75

or, - 25 n = - 105. 5

or, n = 4.2

Solving for m : we get: 3 m + 10 (4.2) = 54.5, or m = 4.1

Hence, the cost of 1 drink = $4.1

And cost of 1 pretzel = $4.22