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 + 31Solve this equation7n1 = 3n +31 + 1= + 1 Add 1to both sides7n + 0 = 3n +327n =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 + 317(8)1 = 3(8) + 3156 1 = 24+ 3155 = 55We 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 + 2455 = 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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