Question

Three families went to the movies together. The Smiths ordered two tubs of popcorn, one plate of nachos, and three drinks. They spent $65. The Langes ordered three tubs of popcorn, one plate of nachos, and five drinks. They spent $85. The Radfords ordered one tub of popcorn, one plate of nachos, and two drinks. They spent $40. Which system of equations matches their night at the movies?

a) 3x+y+2z=65
b) 3x+2y+5z=85
c) x+y+2z=40
d) 2x+y+3z=65

Answer 1

The system of equations that matches the night at the movies for the three families is 3x+2y+5z=85.

Step-by-step explanation:

The system of equations that matches the night at the movies for the three families is b) 3x+2y+5z=85. Let's assign variables to each item: x is the price of one tub of popcorn, y is the price of one plate of nachos, and z is the price of one drink. Based on the information given, the Smiths spent $65 which can be represented by the equation 2x+y+3z=65. The Langes spent $85 which can be represented by the equation 3x+2y+5z=85. The Radfords spent $40 which can be represented by the equation x+y+2z=40. Therefore, the correct equation is 3x+2y+5z=85.