Question

7 years from now Sam's age will be 3 times his daughter's age, and 4 years ago, Sam was 5 times as old as his daughter. Find the simultaneous equations for this situation.

• A. $x-3y=14x-5y=-16$
• B. $x+3y=14x+5y=-16$
• C. $x-5y=14x-3y=-16$
• D. None of the above

Answer 1

The correct option is A $x-3y=14x-5y=-16$

Let the present age of the Sam be $x$ years, and that of his daughter be $y$ years.

7 years from now, their ages will be $(x+7)$ years and $(y+7)$ years.
According to question
$\Rightarrow (x+7)=3(y+7)$
on simplifying we get,
$\Rightarrow x+7=3y+21\Rightarrow \underset{–}{x-3y=14}$

Also, 4 years ago their ages were $(x-4)$ years and $(y-4)$ years.
Again, According to question
$\Rightarrow (x-4)=5(y-4)$
On simplifying we get,
$\Rightarrow x-4=5y-20\Rightarrow \underset{–}{x-5y=-16}$