Question 98222
Let x=length of 1st segment (and length of second one since they are equal), and y=length of 3rd segment



Since the 3rd one is "7 centimeters less than twicw the others", then we have the equation



{{{y=2x-7}}}


Now add up the segments to get 83



{{{x+x+2x-7=83}}} Start with the given equation



{{{4x-7=83}}} Combine like terms on the left side



{{{4x=83+7}}}Add 7 to both sides



{{{4x=90}}} Combine like terms on the right side



{{{x=(90)/(4)}}} Divide both sides by 4 to isolate x




{{{x=45 / 2}}} Reduce


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Answer:

So our answer is {{{x=45 / 2}}}  (which is {{{x=22.5}}} in decimal form)



So the first two segments are 22.5 cm


Now plug in {{{x=22.5}}} to find the 3rd segment



{{{y=2(22.5)-7}}} Plug in {{{x=22.5}}}



{{{y=38}}} Evaluate



So the 3rd segment is 38 cm



Check:


Simply add the 3 segments to find the total length


{{{22.5+22.5+38=83}}} 


Since the segments add to 83, our answer is verified.