Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. The Sheppard family and the Malone family are seeing a movie together in the theater. At the concession stand, Mr. Sheppard paid $38 for 3 large popcorns and 4 large drinks that his family will share. Mrs. Malone bought 3 large popcorns and 3 large drinks and paid $33. How much does each item cost? A large popcorn costs $_____ and a large drink costs $_____.

Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.  The Sheppard family and the Malone family are seeing a movie together in the theater. At the concession stand, Mr. Sheppard paid $38 for 3 large popcorns and  4 large drinks that his family will share. Mrs. Malone bought 3 large popcorns and  3 large drinks and paid $33. How much does each item cost?  A large popcorn costs $_____ and a large drink costs $_____.

Bytelearn · Accepted Answer

Set up equations:  Step 1: Set up the equations based on the information given. Mr. Sheppard's purchase: 3P + 4D = 38 Mrs. Malone's purchase: 3P + 3D = 33 Here, P represents the price of one large popcorn and D represents the price of one large drink. Use elimination:  Step 2: Use elimination to solve the system of equations. Subtract the second equation from the first to eliminate P: (3P + 4D) - (3P + 3D) = 38 - 33 This simplifies to: D = 5 Substitute value:  Step 3: Substitute the value of D back into one of the original equations to find P. Using the second equation: 3P + 3(5) = 33 3P + 15 = 33 3P = 33 - 15 3P = 18 P = 18 / 3 P = 6

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