# The product of Ramu’s age (in years) five years ago with his age (in years) $9$ years later is $15$. Find Ramu’s present age.

Answer

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Hint: Assume Ramu’s age and then try to make an equation out of the information given.

Let Ramu’s present age be$x$years.

According to the question, the product of Ramu’s age five years ago with his age $9$ years later is $15$.

\[\therefore \left( {x - 5} \right)\left( {x + 9} \right) = 15\]

After multiplying,

\[

\Rightarrow {x^2} + 9x - 5x - 45 - 15 = 0 \\

\Rightarrow {x^2} + 4x - 60 = 0 \\

\]

This is a quadratic equation and we have to find the value of$x$.

Now, using factoring (splitting the middle term) method, we get:

\[

\Rightarrow {x^2} + 10x - 6x - 60 = 0 \\

\Rightarrow x\left( {x + 10} \right) - 6\left( {x + 10} \right) = 0 \\

\Rightarrow \left( {x + 10} \right)\left( {x - 6} \right) = 0 \\

\]

Hence, either \[x + 10 = 0\]or \[x - 6 = 0\]

If we take \[x + 10 = 0\], then\[x = - 10\] which is rejected as$x$represents age which cannot be negative.

$

\therefore x - 6 = 0 \\

x = 6 \\

$

Hence, Ramu’s present age is${ 6}$years.

Note: Always try to write the information given in equation form and identify the number of variables present. Also, there are four ways to solve quadratic equations which are factoring, using the square roots, completing the square and the quadratic formula.

Let Ramu’s present age be$x$years.

According to the question, the product of Ramu’s age five years ago with his age $9$ years later is $15$.

\[\therefore \left( {x - 5} \right)\left( {x + 9} \right) = 15\]

After multiplying,

\[

\Rightarrow {x^2} + 9x - 5x - 45 - 15 = 0 \\

\Rightarrow {x^2} + 4x - 60 = 0 \\

\]

This is a quadratic equation and we have to find the value of$x$.

Now, using factoring (splitting the middle term) method, we get:

\[

\Rightarrow {x^2} + 10x - 6x - 60 = 0 \\

\Rightarrow x\left( {x + 10} \right) - 6\left( {x + 10} \right) = 0 \\

\Rightarrow \left( {x + 10} \right)\left( {x - 6} \right) = 0 \\

\]

Hence, either \[x + 10 = 0\]or \[x - 6 = 0\]

If we take \[x + 10 = 0\], then\[x = - 10\] which is rejected as$x$represents age which cannot be negative.

$

\therefore x - 6 = 0 \\

x = 6 \\

$

Hence, Ramu’s present age is${ 6}$years.

Note: Always try to write the information given in equation form and identify the number of variables present. Also, there are four ways to solve quadratic equations which are factoring, using the square roots, completing the square and the quadratic formula.

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