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Natalija [7]
2 years ago
13

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 t

he 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?
Mathematics
1 answer:
Sophie [7]2 years ago
4 0

Answer:

(a)

8x + 2y = 58

4x + 5y = 49

(b)

Bag of popcorn = $6

Candy = $5

Step-by-step explanation:

Given

candy = y

popcorn = x

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

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

Solving (a): System of equation

For Jackson:

8x + 2y = 58

This is done by multiplying each variable by the quantity.

Same will be applied to Cooper's purchase:

Cooper:

4x + 5y = 49

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

This implies that we solve for x and y

8x + 2y = 58 ----- (1)

4x + 5y = 49 -------- (2)

Multiply the second equation by 2

2(4x + 5y = 49)

8x + 10y = 98 -------- (3)

Subtract the (1) from (3)

8x - 8x + 10y - 2y = 98 - 58

10y - 2y = 98 - 58

8y = 40

Solve for y

y = 40/8

y = 5

Substitute 5 for y in (1)

8x + 2y = 58

8x + 2 * 5 = 58

8x + 10 = 58

8x = 58 - 10

8x = 48

Solve for x

x = 48/8

x = 6

This implies:

Bag of popcorn = $6

Candy = $5

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