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June 26th, 2014, 11:28 PM   #1
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Required help to solve algebra 1 homework

Vinay's age after six years will be three-sevenths 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.
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June 27th, 2014, 01:29 AM   #2
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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
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June 27th, 2014, 08:04 AM   #3
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Hello, burgess!

Another approach . . .


Quote:
Vinay's age after six years will be three-seventh 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?

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 $V-10$; his father was $F=10.$

At that time: $\:\dfrac{V-10}{F-10} \:=\:\dfrac{1}{5} \quad\Rightarrow\quad 5V - F \:=\:40\;\;$[2]


Solve the system of equations: $\:V = 18,\;F = 50.$

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