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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.The Maynard family and the Boyer family are seeing a movie together in the theater. At the concession stand, Mr. Maynard paid for large popcorn and large drinks that his family will share. Mrs. Boyer bought large popcorns and large drinks and paid . How much does each item cost?A large popcorn costs and a large drink costs .
Full solution
Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.The Maynard family and the Boyer family are seeing a movie together in the theater. At the concession stand, Mr. Maynard paid for large popcorn and large drinks that his family will share. Mrs. Boyer bought large popcorns and large drinks and paid . How much does each item cost?A large popcorn costs and a large drink costs .
- Define variables: Let's define the variables for the cost of the items.Let be the cost of a large popcorn.Let be the cost of a large drink.
- Write Maynard's equation: Write the equation for the Maynard family's purchase. large popcorn () + large drinks () = So, the equation is:
- Write Boyer's equation: Write the equation for the Boyer family's purchase. large popcorns () + large drinks () = So, the equation is:
- Eliminate variable : We have the system of equations:We need to eliminate one of the variables. Let's eliminate .
- Multiply first equation: Multiply the first equation by to eliminate .
- Add equations: Add the new equation to the second equation to eliminate .x + x - y + y = + \)
- Solve for y: Solve for y.
- Substitute into first equation: Substitute into the first equation to solve for .
- Final solution: We found:A large popcorn costs and a large drink costs .
