Mr. Ohashi's Math Homepage

SOLVING PROBLEMS WITH EQUATIONS

You can use algebra to help you solve story problems. In fact, sometimes the only way to solve a story problem is by either guess & check or by writing an equation!

Suppose we wanted to solve the following problem:

Mr. Ohashi just bought 15 ties and now has 32. How many ties did he have before his purchase?

Step 1: Choose a variable to represent the unknown
The only information we don't know is how many ties Mr. Ohashi had before his purchase. So we write...

Let x = the number of ties Mr. Ohashi had before his purchase

Step 2: Translate the words into an equation
Mr. Ohashi just bought 15 more ties, so we know we are adding. He now has 32, so it must equal 32. The equation must look like...

x + 15 = 32

Step 3: Solve the equation
Now solve the equation like we have solved every algebra equation this year.

Step 4: Answer the question and make sure that your solution makes sense
Since x = 17, we know that Mr. Ohashi had 17 ties before the purchase. This is what the question was asking for, so we write...

Mr. Ohashi had 17 ties before his purchase
If Mr. Ohashi had 17 ties to start, then bought 15 ties, he would have a total of 32 ties! The solution works!

Another Example:

Two identical math books are stacked on top of each other. Then a 5 inch thick geography book is placed on the top. If the stack is 18 inches high, how thick is each math book?

Step 1: Choose a variable to represent the unknown

Let x = the thickness of one math book

Step 2: Translate the words into an equation
2x + 5 = 18

Step 3: Solve the equation

Step 4: Answer the question and make sure that your solution makes sense

Each math book is 6.5 inches thick.
If each math book is 6.5 inches thick and the geography book is 5 inches thick, the three books stacked together would be 6.5 + 6.5 + 5 = 18 inches thick. The solution works!