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Jackson went into a movie theater and bought 8 bags of popcorn (x) and 2 candies (y), costing a total of $58. Cooper went into the same movie theater and bought 4 bags of popcorn (x) and 5 candies (y), costing a total of $49. Write a system of equations that could be used to determine the price of each bag of popcorn and the price of each candy. What is the price of 1 bag of popcorn and 1 candy?

Respuesta :

MrRoyal

Answer:

(a)

[tex]8x + 2y = 58[/tex]

[tex]4x + 5y = 49[/tex]

(b)

Bag of popcorn = $6

Candy = $5

Step-by-step explanation:

Given

[tex]candy = y[/tex]

[tex]popcorn = x[/tex]

Jackson: x = 8; y= 2; Total = 58

Cooper: x = 4; y= 5; Total = 49

Solving (a): System of equation

For Jackson:

[tex]8x + 2y = 58[/tex]

This is done by multiplying each variable by the quantity.

Same will be applied to Cooper's purchase:

Cooper:

[tex]4x + 5y = 49[/tex]

Solving (b): Price of 1 bag of popcorn and 1 candy

This implies that we solve for x and y

[tex]8x + 2y = 58[/tex] ----- (1)

[tex]4x + 5y = 49[/tex] -------- (2)

Multiply the second equation by 2

[tex]2(4x + 5y = 49)[/tex]

[tex]8x + 10y = 98[/tex] -------- (3)

Subtract the (1) from (3)

[tex]8x - 8x + 10y - 2y = 98 - 58[/tex]

[tex]10y - 2y = 98 - 58[/tex]

[tex]8y = 40[/tex]

Solve for y

[tex]y = 40/8[/tex]

[tex]y = 5[/tex]

Substitute 5 for y in (1)

[tex]8x + 2y = 58[/tex]

[tex]8x + 2 * 5 = 58[/tex]

[tex]8x + 10 = 58[/tex]

[tex]8x = 58 - 10[/tex]

[tex]8x = 48[/tex]

Solve for x

[tex]x = 48/8[/tex]

[tex]x = 6[/tex]

This implies:

Bag of popcorn = $6

Candy = $5

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