Question 1163244
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The sum of the ages of Ruth Selma and Tom is one year more than 3 times toms age.the sum of Tom and Selma ages is 2 years more than 3 times Ruth's age.
The sum of Ruth and toms ages is the same as the sum of selmas age and half of ruths age.
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<pre>
Ruth        r
Selma       x
Tom         t
</pre>

{{{system(r+x+t=1+3t,x+t=2+3r,r+t=x+r/2)}}}

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{{{system(r+x-2t=1,-3r+x+t=2,2r+2t=2x+r)}}}


{{{system(r+x-2t=1,3r-x-t=-2,r-2x+2t=0)}}}


From here or earlier, methods can vary, but choosing E1+E3, this gives {{{2r-x=1}}}.  This means, {{{x=2r-1}}}.


Substituting for the expression for x,

{{{system(r+2r-1-2t=1,3r-2r+1-t=-2,r-2(2r-1)+2t=0)}}}


{{{system(3r-2t=2,r-t=-3,r-4r+2+2t=0)}}}


{{{system(3r-2t=2,r-t=-3,-3r+2t=-2)}}}------------here, E1 and E3 are equivalent, so,...


{{{system(3r-2t=2,r-t=-3)}}}


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