Question

Caleb and Jeremiah go to the movie theater and purchase refreshments for their

friends.
Caleb spends a total of $78.25 on 7 bags of popcorn and 2 drinks.
Jeremiah spends a total of $59.75 on 1 bag of popcorn and 10 drinks.
Write a system of equations that can be used to find the price of one bag of popcorn
and the price of one drink.
Using these equations, determine and state the price of a bag of popcorn, to the
nearest cent.

Answer 1

price of each bags of popcorn = $9.75

price of each drinks = $5

Explanation:

Let

price of each bags of popcorn = a

price of each drinks = b

Caleb total cost

7a + 2b = 78.25.......(i)

Jeremiah total cost

a + 10b = 59.75.......(ii)

7a + 2b = 78.25

a + 10b = 59.75

a = 59.75 - 10b

insert the value of a in equation (i)

7a + 2b = 78.25

7( 59.75 - 10b) + 2b = 78.25

418.25 - 70b + 2b = 78.25

418.25 - 68b = 78.25

418.25 - 78.25 = 68b

340 = 68b

b = 340/68

b = 5

Insert the value of b in equation (ii)

a + 10b = 59.75.......(ii)

a + 10 × 5 = 59.75

a = 59.75 - 50

a = 9.75

price of each bags of popcorn = $9.75

price of each drinks = $5