Question 138303
Let the tow parts be x and y.

Given: {{{x + y = 78}}}  and {{{5x/4y = 15/14}}}
{{{5x/4y = 15/14}}}
{{{5x = (15*4y)/14}}}
{{{x = (15*4y)/(14*5)}}}
{{{x = (3*2y)/7}}}
{{{x = 6y/7}}}  --> {{{7x/6 = y}}}

Substitute in the first euwation:
{{{x + y = 78}}} 
{{{x + 7x/6= 78}}}
{{{6x + 7x = 468}}}
{{{13x = 468}}}
{{{x = 36}}}

Check your answer:
{{{x + y = 78}}}
{{{36 + y = 78}}}
{{{y = 42}}}

IS the ratio of 5x/4y = 15/14??  {{{(5*36)/(4*42)}}} = {{{180/168}}} = 15/14  Check!