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Mason and Christian go to the movie theater and purchase refreshments for their friends. Mason spends a total of $45.75 on 3 bags of popcorn and 6 drinks. Christian spends a total of $71.50 on 6 bags of popcorn and 4 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 drink, to the nearest cent.

Respuesta :

Answer:

  • A bag of popcorn costs $10.25
  • One drink costs $2,5

Step-by-step explanation:

Let the cost of a bag of popcorn=p

Let the cost of a drink=d

Mason spends a total of $45.75 on 3 bags of popcorn and 6 drinks.

  • Therefore: 3p+6d=45.75

Christian spends a total of $71.50 on 6 bags of popcorn and 4 drinks.

  • Therefore: 6p+4d=71.50

The required system of equations is:

  • 3p+6d=45.75
  • 6p+4d=71.50

Multiply the first equation by 2 to eliminate p

6p+12d=91.5

6p+4d=71.50

Subtract

8d=20

d=20/8=$2.5

Substitute d=2.5 into any of the equations to obtain p.

6p+12d=91.5

6p+12(2.5)=91.5

6p=91.5-12(2.5)

6p=91.5-30

6p=61.5

Divide both sides by 6

p=$10.25

Therefore:

  • A bag of popcorn costs $10.25
  • One drink costs $2,5