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Bella and Piper go to the movie theater and purchase refreshments for their friends. Bella spends a total of $53.75 on 4 drinks and 3 bags of popcorn. Piper spends a total of $61.25 on 2 drinks and 7 bags of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations, determine and state the price of a bag of popcorn, to the nearest cent.

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KurdishPotato

Answer:

cost of a drink = $9.25

cost of a popcorn = $6.25

Step-by-step explanation:

Bella spends a total of $53.75 on 4 drinks and 3 bags of popcorn

Piper spends a total of $61.25 on 2 drinks and 7 bags of popcorn

Let d represent drinks and p represent popcorn

4d + 3p = $53.75

2d + 7p = $61.25 multiply second equation by -2

-2 × (2d + 7p) = $61.25 ➡-4d - 14p = -$122.50

Now add two equation

-4d - 14p + 4d + 3p = -$122.50 + $53.75 add the like terms (remember -4d will eliminate 4d)

-11p = −$69.25 ➡ 11p = $69.25 divide both sides by 11

p = $6.25 is the price for a bag of popcorn we can use this information to find the price for a drink

4d + 3p = $53.75 replace p with $6.25

4d + 3×6.25 = $53.75

4d + 18.75 = $53.75

4d = $37

d = $9.25