Question

Harper went into a movie theater and bought 10 bags of popcorn and 6 drinks,

Answer 1

Answer:

The price of a drink = $4

The price of a bag of popcorn = $5.5

Step-by-step explanation:

Let p represent popcorn and d represent drink

Harper bought 10 bags of popcorn and 6 drinks and paid $79 ➡ 10p + 6d = $79

Damian bought 3 bags of popcorn and 5 drinks and paid $36.50 ➡ 3p + 5d = $36.50

Now multiply first equation by -3 and second equation by 10

-3 × (10p + 6d) = $79 ➡ -30p - 18d = -$237

10 × (3p + 5d) = $36.50 ➡ 30p + 50d = $365

Now add the new equationd

30p + 50d -30p - 18d = $365 - $237 (-30p will eliminate 30p)

32d = $128 divide both sides of the equation by 32

32 ÷ 32d = 32 ÷ $128 ➡ d = 4

If d = 4 that means a drink costs $4 we can use this information to find the price of a bag of popcorn

3p + 5d = $36.50 (replace d with 4)

3p + 4×5 = $36.50

3p + 20 = $36.50

3p = $36.50 - 20

3p = 16.50 divide both sides by 3

p = $5.5