Write a system of equations to represent this problem and determine the unit price of each item purchased? Define your variables.
Alvin, Theodore, and Simon went to the movies. Alvin bought 2 boxes of popcorn, 4 cherry slushies, and 2 boxes of candy. He spent $49.50. Theodore bought 3 boxes of popcorn, 2 cherry slushies, and 4 boxes of candy. He spent $57.75. Simon bought 3 boxes of popcorn, 3 cherry slushies, and 1 box of candy. He spent $38.50.
Alvin, Theodore, and Simon went to the movies. Alvin bought 2 boxes of popcorn, 4 cherry slushies, and 2 boxes of candy. He spent $49.50. Theodore bought 3 boxes of popcorn, 2 cherry slushies, and 4 boxes of candy. He spent $57.75. Simon bought 3 boxes of popcorn, 3 cherry slushies, and 1 box of candy. He spent $38.50.
1 Answer
The cost of each box of popcorn is
The cost of each cherry sushi is
The cost of each box of candy is
Explanation:
Alvin, Theodore, and Simon went to the movies. Alvin bought 2 boxes of popcorn, 4 cherry sushies, and 2 boxes of candy. He spent $49.50. Theodore bought 3 boxes of popcorn, 2 cherry sushies, and 4 boxes of candy. He spent $57.75. Simon bought 3 boxes of popcorn, 3 cherry sushies, and 1 box of candy. He spent $38.50.
Let the cost of each box of popcorn be
Let the cost of each cherry sushi be
Let the cost of each box of candy be
Given That :
Alvin bought 2 boxes of popcorn, 4 cherry sushies, and 2 boxes of candy. He spent $49.50.
Theodore bought 3 boxes of popcorn, 2 cherry sushies, and 4 boxes of candy. He spent $57.75.
Simon bought 3 boxes of popcorn, 3 cherry sushies, and 1 box of candy. He spent $38.50.
The set of equations with three variables to solve is:
We can solve this set of three equations by elimination and substitution method.
Consider equations (2) and (3) to eliminate
Subtract (3) from (2). That gives:
(2) - (3)
Consider equation (1) and (3) to eliminate
(1) x 3 - (3) x 2 will give:
Now consider (4) and (5) to eliminate
(4) x 6 + (5) gives:
Substitute value of
Substitute value of
Cross check by substituting in (2)