Ralph is 3 times as old as Sara. In 4 years, Ralph will be only twice as old as Sara will be then. Find Ralph's age now. Ralph's age is _____.

Let
R = Ralph's age
S = Sara's age

First statement is translated as:
S = 3R

Second statement is translated as:
S + 4 = 2(R + 4)

Use the first equation to be substituted into the second one in terms of R which is the one we are actually going to solve for Ralph's age.
Since S = 3R, then
3R + 4 = 2(R + 4)
3R + 4 = 2R + 8
3R - 2R = 8 - 4
R = 4 years old

Answer Link

ColinJacobus ColinJacobus · Answer 2 · 2019-10-05T06:08:55+02:00

Answer: The required present age of Ralph is 12 years.

Step-by-step explanation: Given that Ralph is 3 times as old as Sara and in 4 years, Ralph will be only twice as old as Sara will be then.

We are to find the present age of Ralph.

Let r and s represents the present ages of Ralph and Sara respectively.

According to the given information, we have

[tex]r=3s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\r+4=2(s+4)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

Substituting the value of r from equation (i) in equation (ii), we get

[tex]3s+4=2(s+4)\\\\\Rightarrow 3s+4=2s+8\\\\\Rightarrow 3s-2s=8-4\\\\\Rightarrow s=4.[/tex]

Therefore, from equation (i), we get

[tex]r=3\times4=12.[/tex]

Thus, the required present age of Ralph is 12 years.