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The sum of two numbers is 119. If 4 times the smaller number is subtracted from the larger number the result is nine. Find the two numbers.

 Jan 27, 2020
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The sum of two numbers is 119. If 4 times the smaller number is subtracted from the larger number the result is nine. Find the two numbers.   

 

Call the numbers X (the larger) and Y (the smaller). 

                                                                                        X + Y  =  119          (line 1)

                                                                                        X – 4Y  =    9          (line 2)    

 

                                                                                       X + Y     =   119        (line 1) 

multiply both sides of line 2 by negative one               – (X – 4Y)  =   –9        

                                                                                      –X + 4Y    =   –9        (line 3) 

add line 1 and line 3                                                               5Y   =  110     

divide both sides by 5                                                               Y  =  22       this is the smaller number                       

 

substitute 22 for Y in line 1                                                X + 22  =  119                        

subtract 22 from both sides                                                       X  =  97       this is the larger number                 

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 Jan 27, 2020
edited by Guest  Jan 27, 2020

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