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Morgarella [4.7K]
2 years ago
9

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 _____.
Mathematics
2 answers:
IgorLugansk [536]2 years ago
7 0
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
Y_Kistochka [10]2 years ago
4 0

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

r=3s~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\r+4=2(s+4)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)

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

3s+4=2(s+4)\\\\\Rightarrow 3s+4=2s+8\\\\\Rightarrow 3s-2s=8-4\\\\\Rightarrow s=4.

Therefore, from equation (i), we get

r=3\times4=12.

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

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