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Translate each into a variable equation AND solve: The sum of two numbers is two. The difference between eight and twice the smaller number is two less than four times the larger. Find the two numbers.

 Oct 18, 2017
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Let x be the smaller number and y be the larger.....so....

 

x + y  = 2    →   y  =  2 - x      (1)

 

" The difference between eight and twice the smaller number is two less than four times the larger"

translates as         [ 8 - 2x ]  + 2  =  4y   (2)

 

Put  (1)  into (2)   and we have that

 

[8 - 2x ] + 2  = 4 [ 2 - x ]      simplify

 

10 - 2x   =  8 - 4x           add 4x to both sides, subract 10 from both sides

 

2x  = -2                  divide both sides by 2

 

x  = -1

 

Sub this into (1)  to find y

 

y  =  2  - (-1)   =  2 + 1  =  3

 

 

cool cool cool

 Oct 18, 2017
edited by CPhill  Oct 18, 2017

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