Question 190058
Let n be the first number and m be the second number.
1) {{{n = 4M}}} "One number (n) is four time as large as another (m)"
2) {{{1/n + 1/m = 5/12}}} "The sum of their reciprocals is {{{5/12}}}" Substitute {{{n = 4m}}} into the second equation.
{{{1/4m + 1/m = 5/12}}} Add the fractions on the left side.
{{{(5)/4m = 5/12}}} Solve for m.Multiply both sides by 4m.
{{{5 = 4m(5/12)}}} Multiply both sides by {{{12/5}}}
{{{5(12/5) = 4m}}} Divide both sides by 4.
{{{12/4 = m}}}
{{{m = 3}}}
{{{n = 4m}}}
{{{n = 4(3)}}}
{{{n = 12}}}
The two numbers are 3 and 12.