Question

Sam is 2 years and his mother is 28 years old. In how many years will Sam's mother be 3 times as old as he will be?

Answer 1

Answer:

$x=13$

Step-by-step explanation:

Let:

$A_s=Age\hspace{3}of\hspace{3}Sam\\A_m=Age\hspace{3}of\hspace{3}Sam's\hspace{3}mother\\x=Years\hspace{3}required\hspace{3}for\hspace{3}Sam's\hspace{3}mother\hspace{3}be\hspace{3}3\hspace{3}times\hspace{3}as\hspace{3}old\hspace{3}as\hspace{3}sam\hspace{3}will\hspace{3}be$

Now, let's write the problem in form of an algebraic equation. Basically, the future age will be the current age plus x quantity of years. So mathematically we can calculate in how many years will Sam's mother be 3 times as old as he will be as:

$A_m+x=3(A_s+x)$

Solving for x:

$A_m+x=3A_s+3x\\3x-x=A_m-3A_s\\2x=A_m-3A_s\\x=\frac{A_m-3A_s}{2}$

Replacing the values of $A_m$ and $A_s$

$x=\frac{28-3(2)}{2}=\frac{28-6}{2}=\frac{22}{2}=11$

Hence, the years required for Sam's mother be 3 times as old as sam will be is 11

Answer 2

When Sam is 13 his mother will be 39 which is 3 times as old as he is. So Sam's mother will be 3 times as old as Sam will be in 11 years. (Your answer is 11 years.)