Problem solving

Step 1: Introduce variables to represent unknown values.

Step 2: Form a system of equations using the variables.

Step 3: Solve the system.

Step 4: Answer the problem and verify the solution.

Example 1

Your are running a concession stand, and are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the day you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. How many hot dogs were sold and how many sodas were sold?

Step 1 

x = the number of hot dogs sold

y= the number of sodas sold

Step 2

1.50x + 0.50y = 78.50

x + y = 87

Step 3 

Solve the system.

(35, 52) is the solution to the system.

Step 4

35 hot dogs were sold and 52 sodas were sold.

Verify answer.

If both equations check properly then the answers are correct.

Example 2 

You are going to get lunch with a friend. You order three tacos and three burritos and your total bill is $11.25. Your friend’s bill is $10.00 for four tacos and two burritos. How much do tacos cost and how much do burritos cost?

Step 1 

x= price of 1 taco

y= price of 1 burrito

Step 2

3x + 3y = 11.25  (Equation representing your lunch)

4x + 2y = 10   (Equation representing your friend’s lunch)

Step 3 

Solve the system.

The solution to the system is x= 1.25 and y= 2.5.

Step 4

One taco costs $1.25 and one burrito costs $2.50.

Verify answer.

Why

By knowing how to find solutions to word problems it helps to find unknown variables that can be in real life situations. For an example, if you are trying to find the cost of something that is not clearly stated, you can easily find out by using your knowledge of systems of equations.