Question

Logan and Jack go to the movie theater and purchase refreshments for their friends. Logan spends a total of $118.50 on 6 drinks and 10 bags of popcorn. Jack spends a total of $27.50 on 2 drinks and 2 bags of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations, determine and state the price of a drink, to the nearest cent.

Answer 1

6d + 10p = 118.50

2d + 2p = 27.50

drink = $4.75

Explanation:

You can solve the system of equations above by using the elimination method. This method involves using positive and negative coefficients of one variable to eliminate it from the equation and solve for the remaining variable. Since you are going to be adding the systems together, you need to multiply one of the equations by a negative factor to eliminate one of the variables.

Multiply by a factor of '-3': -3(2d + 2p = 27.50) = -6d - 6p = -82.50

Add the system: 6d + 10p = 118.50

+ -6d - 6p = -82.50

4p = 36 or p = $9 for popcorn

Since we are solving for the cost of a drink, we can put in the value of $9 for the variable 'p' and solve for 'd':

2d + 2(9) = 27.50 or 2d + 18 = 27.50

Subtract 18 from both sides: 2d + 18 - 18 = 27.50 - 18 or 2d = 9.50

Divide and solve for 'd': 2d/2 = 9.50/2 or d = $4.75