Question

(HELP QUICKLY PLEASE) Liam went into a movie theater and bought 9 bags of popcorn and 8 drinks, costing a total of $97.50. Jacob went into the same movie theater and bought 5 bags of popcorn and 4 drinks, costing a total of $51.50. Determine the price of each bag of popcorn and the price of each drink.

Each bag of popcorn costs $____
and each drink costs $_____

Answer 1

How to calculate the number of popcorn and drink?

In a movie theater, Liam spent $97.50 on 9 bags of popcorn and 8 drinks. As follows:

• 9p + 8d = 97.50

Jacob visited the same movie theater and spent $51.50 on 5 bags of popcorn and 4 drinks. As follows:

• 5p + 4d = 51.50

SOLUTION

where P = popcorn and d = drink

The equations will be:

9p + 8d = 97.50 (multiply by 5)

• 9 x 5 = 45p
• 8 x 5 = 40d
• 97.50 × 5 = 487.50

5p + 4d = 51.50 (multiply by 9)

• 5 x 9 = 45p
• 4 x 9 = 36d
• 51.50 x 9 = 463.50

THEN SUBTRACT

45p + 40d = 487.50

45p + 36d = 463.50

• 45p - 45p = X
• 40d - 36d = 4d
• 487.50 - 463.50 = 24

4d = 24 ÷ 4

• 4 ÷ 4 = 1/d
• 24 ÷ 4 = 6

DRINK = $6

Since 9p + 8d = 97.50

• 9p + 8(6) = 97.50
• 9p + 48 = 97.50
• 9p = 97.50 - 48.00

POPCORN = $5.50

The cost of the drink is $6 and each bag of popcorn is $5.50.

Answer 2

Each bag of popcorn is $5.50

Each bag of popcorn is $5.50 and the drink is $6.

Explanation:

Liam went into a movie theater and bought 9 bags of popcorn and 8 drinks costing a total of $97.50. This will be:

9p + 8d = 97.50

Jacob went into the same movie theater and bought 5 bags of popcorn and 4 drinks, costing a total of $51.50. This will be:

5p + 4d = 51.50

where P = popcorn

d = drink

The equations will be:

9p + 8d = 97.50

5p + 4d = 51.50

Multiply equation i by 5

Multiply equation ii by 9

45p + 40d = 487.50

45p + 36d = 463.50

Subtract

4d = 24

Divide.

d = 24/4

d = 6

Drink = $6

Since 9p + 8d = 97.50

9p + 8(6) = 97.50

9p + 48 = 97.50

9p = 97.50 - 48

p = $5.50

Popcorn cost $5.50.

hope it helps<3