SOLUTION: 41 is added to a mystery number. The result is multiplied by 9. After that 47 is subtracted. The final value is 979. What was the mystery number at the beginning?

Algebra ->  Test -> SOLUTION: 41 is added to a mystery number. The result is multiplied by 9. After that 47 is subtracted. The final value is 979. What was the mystery number at the beginning?      Log On


   

Question 1197193: 41 is added to a mystery number. The result is multiplied by 9. After that 47 is subtracted. The final value is 979. What was the mystery number at the beginning?
Found 3 solutions by math_tutor2020, Theo, ikleyn:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

x = mystery number
x+41 = add on 41
9(x+41) = multiply by 9
9(x+41)-47 = subtract off 47
9(x+41)-47 = 979

Solve for x
We'll follow the steps in reverse to undo each thing we applied
So we'll start to undo the "subtract off 47" by adding 47 to both sides
Then we undo the "multiply by 9" to divide both sides by 9
The last thing we undo is the "plus 41" by subtracting 41 from both sides

This is what the steps look like
9(x+41)-47 = 979
9(x+41)-47+47 = 979+47
9(x+41) = 1026
9(x+41)/9 = 1026/9
x+41 = 114
x+41-41 = 114-41
x = 73

The mystery number is 73

Check:
73
73+41 = 114
9*114 = 1026
1026-47 = 979

Another way to check is to replace x with 73 in the equation we set up
9(x+41)-47 = 979
9(73+41)-47 = 979
9(114)-47 = 979
1026-47 = 979
979 = 979
The answer is confirmed.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x = the mystery number.
equation becomes:
(x + 41) * 9 - 47 = 979
simplify to get:
9x + 369 - 47 = 979
combine like terms to get:
9x + 322 = 979
subtract 322 from both sides of the equation to get:
9x = 979 - 322 = 657
divide both sides of the equation by 9 to get:
x = 657/9 = 73
that's the mystery number.

confirm by replacing x in the original equation to get:
(73 + 41) * 9 - 47 = 979
combine like terms within the parentheses to get:
114 * 9 - 47 = 979
simplify to get:
1026 - 47 = 979
combine like terms to get:
979 = 979
this confirms the solution is correct.



Answer by ikleyn(52815) About Me  (Show Source):
You can put this solution on YOUR website!
.
41 is added to a mystery number. The result is multiplied by 9. After that 47 is subtracted.
The final value is 979. What was the mystery number at the beginning?
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            Usually, even young students of the  4-th grade level can solve such problems using a backward method
            and making inverse operations in the reverse order - without using equations. 


Solving this way, you make three steps:


    (1)  You add 47 to 979, and you obtain 47 + 979 = 1026.


    (2)  Next you divide 1026 by 9, and you get  1026/9 = 114.

    (3)  Now your final step is to subtract 41 from 114.

         By doing it, you obtain your miracle number  114 - 41 = 73.


ANSWER.  The miracle number is 73.

Solved for the  4-th grade level step by step without using equations,  with full explanations.