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

Question

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.

Answer 1

If we denote by x boxes of popcorn, y cherry slushies, and z boxes of candy, then we have the follwoing systen of 3 linear equations.

2x+4y+2z=49.50

3x+2y+4z=57.75

3x+y        =38.50

If you solve this system you find the unit price for each item.

x = 11.16, y=5.015, z=3.56

 

Answer 2

If you let p, s and c represent the unit prices of popcorn, slushies and candy respectively, the 3 equations would be:

2p+4s+2c=49.50

3p+2s+4c=57.75

3p+3s+c=38.50

Then it's just a matter of substituting successive variables in terms of the others. For example 

3p+3s+c=38.50 => c=38.50-(3p+3s)

That value can be plugged into one of the two remaining expressions and either p or s determined in terms of the other. Then both of those equivalencies plugged into the third equation and solve for that variable. Once done, then work backwards to determine value of the other two.