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June 26th, 2014, 11:28 PM  #1 
Member Joined: Jun 2014 From: Brighton Posts: 49 Thanks: 2  Required help to solve algebra 1 homework
Vinay's age after six years will be threesevenths of his father's age. Ten years ago, the ratio of their ages was 1:5. What is Vinay's father's age at present?
Last edited by skipjack; June 27th, 2014 at 07:33 PM. 
June 27th, 2014, 01:29 AM  #2 
Newbie Joined: Jun 2014 From: India Posts: 2 Thanks: 0  Solution to Age problem
Let Vinay’s age before 10 years be x. So his father’s age before 10 years will be 5x. After 6 years Vinay’s age will be x+10+6 = x+16 and father’s will be 5x +16. As per the given condition; x+16=3/7*(5x+16) 7(x+16)=3(5x+16) 7x+112=15x+48 64=8x X=8 Father’s present age is 5x+10=5*8+10=40+10 = 50 years 
June 27th, 2014, 08:04 AM  #3  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Hello, burgess! Another approach . . . Quote:
Let $V$ = Vinday's present age. Let $F$ = his father's present age. "After 6 years, Vinay's age will be 3/7 of his father's age." In 6 years, they will both be 6 years older. Vinay will be $V+6$; his father will be $F+6.$ At that time: $\:V+6 \:=\:\frac{3}{7}(F+6) \quad\Rightarrow\quad 7V  3F \:=\:24\;\;$[1] "Ten years ago, the ratio of their ages was 1:5." Ten years ago, they were both 10 years younger. Vinay was $V10$; his father was $F=10.$ At that time: $\:\dfrac{V10}{F10} \:=\:\dfrac{1}{5} \quad\Rightarrow\quad 5V  F \:=\:40\;\;$[2] Solve the system of equations: $\:V = 18,\;F = 50.$  

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