Question 563449
Let 
First Number = {{{x+1}}}
Second Number={{{x+2}}}
Third Number = {{{x+3}}}


Given
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sum of the first plus one-third of the second plus three-eighths of the third is 25.
{{{(x+1)+(1/3)(x+2)+(3/8)(x+3)=25}}}
{{{(x+1)+(x+2)/3+((3)(x+3))/8=25}}}
{{{(x+1)+(x+2)/3+((3)(x+3))/8=25}}}
{{{(x+1)+(x+2)/3+(3x+9)/8=25}}}

Take LCD on R.H.S.
{{{(24(x+1)+8(x+2)+3(3x+9))/24=25}}}
{{{(24x+24+8x+16+9x+27)/24=25}}}
{{{(41x+67)/24=25}}}
Multiply by 24 both sides of above equation
{{{(24)(41x+67)/24=(25)(24)}}}
{{{cross(24)(41x+67)/cross(24)=600}}}
{{{41x+67=600}}}
{{{41x=600-67}}}
{{{41x=533}}}
Divide by 41 both sides of above equation
{{{41x/41=533/41}}}
{{{cross(41)x/cross(41)=cross(533)/cross(41)}}}
{{{x=13}}}



First Number = {{{x+1}}} = {{{13+1}}} = {{{14}}} 
Second Number={{{x+2}}} = {{{13+2}}} = {{{15}}}
Third Number = {{{x+3}}} = {{{13+3}}} = {{{16}}}

Check
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sum of the first plus one-third of the second plus three-eighths of the third is 25.
{{{14+(1/3)(15)+(3/8)(16)=25}}}
{{{14+15/3+48/8=25}}}
{{{14+cross(15)/cross(3)+cross(48)/cross(8)=25}}}
{{{14+5+6=25}}}
{{{25=25}}}