Question

chiro is five years older than sophia. The product of their ages four years from now os 50. find their present age.​

Answer 1

shophia = 1 years

Chiro = 6 years

Answer 2

Given,

Consider the age of Chiro is x years and age of Sophia is y years.

$\[\begin{array}{l}x = y + 5 - - - - \left( 1 \right)\\\left( {x + 4} \right)\left( {y + 4} \right) = 50 - - - \left( 2 \right)\end{array}\]$

Solution,

Put the value of x from equation 1 in equation 2.

$\[\begin{array}{l}\left( {x + 4} \right)\left( {y + 4} \right) = 50\\ \Rightarrow \left( {y + 5 + 4} \right)\left( {y + 4} \right) = 50\\ \Rightarrow \left( {y + 9} \right)\left( {y + 4} \right) = 50\\ \Rightarrow {y^2} + 13y + 36 = 50\\ \Rightarrow {y^2} + 13y - 14 = 0\\ \Rightarrow {y^2} + 14y - y - 14 = 0\\ \Rightarrow y\left( {y + 14} \right) - 1\left( {y + 14} \right) = 0\\ \Rightarrow \left( {y - 1} \right)\left( {y + 14} \right) = 0\\ \Rightarrow y = 1, - 14\end{array}\]$

Put the y value in in equation 1,

$\[\begin{array}{l}x = y + 5\\ \Rightarrow x = 1 + 5\\ \Rightarrow x = 6\end{array}\]$

Hence the age of Chiro is 6 years and age of Sophia is 1 year.