Math Is Easy - Use Algebra To Solve Word Problem 5!

 

If 1 is subtracted from seven times a certain number, the result is the same as if 31 is added to three times the number. Find the number. (Note 1)

 

If we let n represent the number to be found, the sentence “If 1 is subtracted from seven times a certain number, the result is the same as if 31 is added to three times the number.” can be translated into the following algebraic equation:

7n – 1 = 3n + 31

 

Solve this equation

7n – 1 =     3n + 31

     + 1 =         +    1 Add 1 to both sides

7n + 0 =    3n +  32

7n       =    3n +  32

 

  7n     =     3n + 32

- 3n     =  - 3n         Subtract 3n from each side

  4n      =    0n + 32

  4n      =            32

 

  4n/4    =           32/4 Divide each side by 4

    n       =             8

 

Now we substitute the solution for n into the original equation to see if it works.

7n    – 1 = 3n   + 31

7(8) – 1 = 3(8) + 31

56    – 1 =  24  + 31

55         =  55

 

We must also see if the solution works in the original  problem statement.

If 1 is subtracted from seven times a certain number, the result is the same as if 31 is added to three times the number.

If 1 is subtracted from seven times a certain number (7 X 8), the result is the same as if 31 is added to three times the number (3 X 8).

If 1 is subtracted from seven times a certain number (56), the result is the same as if 31 is added to three times the number (24).

If 1 is subtracted from 56, the result is the same as if 31 is added to 24.

56 – 1 = 31 + 24

55 = 55      

 

We have just solved a first degree equation.

 

(Note 1)

The source for the problem statement is:

“Intermediate Algebra  For College Students” by Jerome E. Kaufman

 


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