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 thenumber. (Note 1)

If we let n represent the number to be found, the sentenceIf 1 is subtracted from seven times a certain number, the result is the sameas if 31 is added to three times the number. can be translated into thefollowing algebraic equation:

7n1 = 3n + 31

Solve this equation

7n1 = 3n +31

+ 1= + 1 Add 1to 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 solutionfor 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 theoriginal 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 (7X 8), the result is the same as if 31 is added to three times the number (3 X8).

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 if31 is added to 24.

561 = 31 + 24

55 = 55

We have just solved a first degree equation.

(Note1)

The source for the problem statement is:

Intermediate AlgebraFor College Students by Jerome E. Kaufman


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