Question

A father tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” Select the algebraic equations that represent this situation.

• A. $x–7y=-42$
• B. $x–3y=6$
• C. $7x–2y=-32$
• D. $x+3y=-6$

Answer 1

Answer: (A), (B)

The correct options are
A

$x–7y=-42$

B

$x–3y=6$

Let, father's age be $x$ and daughter's age be $y$.

Their ages 7 years ago were $x-7$ and $y-7$

Accorning to first condition,
$\Rightarrow x-7=7(y-7)$
$\Rightarrow x–7=7y–49$
$\Rightarrow x–7y=-42$

Their ages three years from now wil be $x+3$ and $y+3$

According to second condition,
$\Rightarrow (x+3)=3(y+3)$
$\Rightarrow x+3=3y+9$
$\Rightarrow x–3y=6$

Thus, the given conditions can be algebraically represented as:
$x–7y=-42$ and $x–3y=6$