WRITING A VERBAL DESCRIPTION OF A TWO STEP EQUATION

Example 1 : 

Write a corresponding real-world problem to represent 5x + 50 = 120.

Solution :

Step 1 : 

Analyze what each part of the equation means mathematically.

x is the solution of the problem, the quantity we are looking for.

5x means that, for a reason given in the problem, the quantity we are looking for is multiplied by 5.

+ 50 means that, for a reason given in the problem, 50 is added to 5x.

= 120 means that after multiplying the solution x by 5 and adding 50 to it, the result is 120.

Step 2 :

Think of some different situations in which a quantity x might be multiplied by 5.

You have x number of books, each weighing 5 pounds, and you want to know their total weight.

or

You save $5 each week for x weeks and want to know the total amount you have saved.

Step 3 : 

Build on the situation and adjust it to create a verbal description that takes all of the information of the equation into account.

• A publisher ships a package of x number of books each weighing 5 pounds, plus a second package weighing 50 pounds. The total weight of both packages is 120 pounds. How many books are being shipped ?

• Leon receives a birthday gift of $50 from his parents and decides to save it. Each week he adds $5 to his savings. How many weeks will it take for him to save $120 ?

Example 2 : 

Write a corresponding real-world problem to represent 40 + 12m = 460.

Solution :

Step 1 : 

Analyze what each part of the equation means mathematically.

m is the solution of the problem, the quantity we are looking for.

12m means that, for a reason given in the problem, the quantity we are looking for is multiplied by 12.

+ 40 means that, for a reason given in the problem, 40 is added to 5x.

= 460 means that after multiplying the solution m by 12 and adding 40 to it, the result is 460.

Step 2 :

Think of a situation in which a quantity m might be multiplied by 12.

You are paying m dollars per month to a metro gym and you want to know how much you pay for one year.

Step 3 : 

Build on the situation and adjust it to create a verbal description that takes all of the information of the equation into account.

A one-year membership to Metro Gym costs $460. There is a fee of $40 when you join, and the rest is paid monthly. How much you will pay monthly for the yearlong membership ? 

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