Question 453606
Let x be that number.



The problem translates to the equation: {{{(5+x)/(8-x)=8/5}}}



{{{(5+x)/(8-x)=8/5}}} Start with the given equation.



{{{5(5+x)=8(8-x)}}} Cross multiply.



{{{25+5x=64-8x}}} Distribute.



{{{5x=64-8x-25}}} Subtract {{{25}}} from both sides.



{{{5x+8x=64-25}}} Add {{{8x}}} to both sides.



{{{13x=64-25}}} Combine like terms on the left side.



{{{13x=39}}} Combine like terms on the right side.



{{{x=(39)/(13)}}} Divide both sides by {{{13}}} to isolate {{{x}}}.



{{{x=3}}} Reduce.



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Answer:


So the solution is {{{x=3}}}