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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