Question

Noah went into a movie theater and bought 9 drinks and 4 candies, costing a total of $60. Nachelle went into the same movie theater and bought 10 drinks and 2 candies, costing a total of $57.50. Determine the price of each drink and the price of each candy.

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Answer 1

See below.

Explanation:

Let the price of drinks be x and the price of candies be y.

Condition # 1:

9x + 4y = 60 --------------------(1)

Condition # 2:

10x + 2y = 57.50 --------------(2)

• Multiply Eq. (2) by 2

2(10x + 2y) = 57.50*2

20x + 4y = 115 --------------(3)

• Subtract Eq. (3) from (1)

9x + 4y - 20x - 4y = 60 - 115

9x - 20x = -55

-11x = -55

11x = 55

• Divide both sides by 11

x = 55/11

x = $5

Put x = 5 in Eq. (1)

9(5) + 4y = 60

45 + 4y = 60

• Subtract 45 to both sides

4y = 60 - 45

4y = 15

• Divide both sides by 4

y = 15/4

y = $3.75

So, the cost of one drink is $5 and the cost of one candy is $3.75.

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