# Write a system of equations to represent this problem and determine the unit price of each item purchased? Define your variables.

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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)