Take Me Out to the Ballgame

Mixture Problems in 2 Variables

The Problem – Stadium Chow

• On his very first trip to the concession stand, Jim bought 5 hot dogs and 7 drinks for a total of $23.00.

• On his second trip to the concession stand, Jim bought 3 hot hogs and 10 drinks for a total of $22.50.

• What is the price of a hot dog?

• What is the price of a drink?

Set up the Problem

Let h = price of one hot dog

Let d = price of one drink

You can use x and y if you prefer.

Using h and d helps you to realize what variable you have solved for when you get your answer.

Now Write the Story

5 hot dogs and 7 drinks cost $23.00

5h + 7d = 23.00

3 hot hogs and 10 drinks cost $22.50

3h + 10d = 22.50

Solve the Problem

- 3 | 5h + 7d = 23.00

+ 5 | 3h + 10d = 22.50

- 15h - 21d = - 69.00

+15h + 50d = 112.50

29d = 43.50

d = 1.50

Find the 2nd Answer

Substitute the value of d into the first equation

5h + 7 ( 1.50 ) = 23.00

5h + 10.50 = 23.00

5h = 23.00 – 10.50

5h = 12.50

h = 2.50

Answer the Question

What is the price of a hot dog? h = 2.50

What is the price of a drink? d = 1.50

The price of a hot dog is $2.50.

The price of a drink is $1.50.

Careful! Some of these are confusing!

A supplement calls for:

50 mg of vitamin C and 10 mg of vitamin D.

Your pharmacy stocks two compounds that can be mixed to create the supplement.

#1) 80% vitamin C and 10% vitamin D

#2) 40% vitamin C and 20% vitamin D.

How many mg of each compound should be used?

Base your equations on the totals

A supplement calls for

50 mg of vitamin C

10 mg of vitamin D.

Make your first equation about vitamin C

and your second equation about vitamin D

Call your compounds x and y

Let x = mg of #1 and y = mg of #2

Compound #1: 80% vitamin C and 10% vitamin D

Compound #2: 40% vitamin C and 20% vitamin D.

Vitamin C: .80x + .40y = 50

Vitamin D: .10x + .20y = 10

Notice the columns

Vitamin C: .80x + .40y = 50

Vitamin D: .10x + .20y = 10

#1

#2

Compound #1: 80% vitamin C and 10% vitamin DCompound #2: 40% vitamin C and 20% vitamin D.

Two Variable Story Problems

Most of these types of problems just write themselves!

If the information is confusing, base the equations on the totals you are given.

Be sure that you have answered the question that is asked!