Question

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.

Answer 1

Answer:

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