arper went into a movie theater and bought 10 bags of popcorn and 6 drinks, costing a total of $79. Damian went into the same mo
vie theater and bought 3 bags of popcorn and 5 drinks, costing a total of $36.50. Write a system of equations that could be used to determine the price of each bag of popcorn and the price of each drink. Define the variables that you use to write the system.
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
