Question 515301
Let s = Sunitha's present age
Let f = father's age
:
Write an equation for exactly what it says
:
"Sunitha is 19 years younger than her father."
s = f - 19
:
" After 5 years, their ages will be in the ratio 2:3."
{{{((s+5))/((f+5))}}} = {{{2/3}}}
cross multiply
3(s+5) = 2(f+5)
3s + 15 = 2f + 10
3s = 2f + 10 - 15
3s = 2f - 5
From the 1st statement, replace s with (f-19)
3(f-19) = 2f - 5
3f - 57 = 2f - 5
3f - 2s = -5 + 57
f = 52 is F's age
then
52 - 19 = 33 is S's age


:
You can confirm this by substitution in the 2nd statement: {{{38/57}}} = {{{2/3}}}