Question 672601

A father's age is now three times that of his elder daughter. Five years back, his age was eight times that of his younger daughter. If the difference of ages of the two daughters is 5 years, what is the age of the father now?


Let the current age of the father be F, and current age of younger daughter, Y
Then elder daughter is currently: {{{(1/3)F}}}, or {{{F/3}}}
Also, F – 5 = 8(Y – 5) ---- F – 5 = 8Y – 40 ------ F - 8Y = - 40  + 5 ---- F - 8Y = - 35 ------ eq (i)
Since elder is older, then: {{{F/3 - Y = 5}}} ----- {{{Y = F/3 - 5}}} ---- eq (ii)


{{{F - 8(F/3 - 5) = - 35}}} ------ Substituting {{{F/3 - 5}}} for Y in eq (i)


{{{F - 8F/3 + 40 = - 35}}} 


3F - 8F + 120 = - 105 ------- Multiplying by LCD, 3


3F - 8F = - 105 - 120 


- 5F = - 225


F, or father’s current age = {{{(- 225)/- 5}}}, or {{{highlight_green(45)}}}


Send comments and “thank-yous” to “D” at MathMadEzy@aol.com