Question

The sum of the ages of three sisters Rhoda , Sally and Tabitha is 39 years, sally is twice as old as Tabitha and one and a half times as old as Rhoda . Determine their ages

Answer 1

Let's denote the ages of the three sisters as follows:
- Let \( R \) be the age of Rhoda.
- Let \( S \) be the age of Sally.
- Let \( T \) be the age of Tabitha.

From the problem statement, we have the following equations:

1. The sum of their ages is 39 years:
\[
R + S + T = 39
\]

2. Sally is twice as old as Tabitha:
\[
S = 2T
\]

3. Sally is one and a half times as old as Rhoda:
\[
S = \frac{3}{2} R
\]

Now, we can substitute \( S \) from the second equation into the first and third equations.

Substituting \( S = 2T \) into the first equation:
\[
R + 2T + T = 39
\]
This simplifies to:
\[
R + 3T = 39 \quad \text{(Equation 4)}
\]

Now, substituting \( S = 2T \) into the third equation:
\[
2T = \frac{3}{2} R
\]
Multiplying both sides by 2 to eliminate the fraction:
\[
4T = 3R
\]
This gives us:
\[
R = \frac{4}{3} T \quad \text{(Equation 5)}
\]

Now we can substitute Equation 5 into Equation 4:
\[
\frac{4}{3} T + 3T = 39
\]
To combine the terms, we need a common denominator:
\[
\frac{4}{3} T + \frac{9}{3} T = 39
\]
This simplifies to:
\[
\frac{13}{3} T = 39
\]
Now, multiply both sides by 3:
\[
13T = 117
\]
Dividing by 13:
\[
T = 9
\]

Now that we have Tabitha's age, we can find Sally's and Rhoda's ages.

Using \( T = 9 \) in Equation 2 to find \( S \):
\[
S = 2T = 2 \times 9 = 18
\]

Using \( T = 9 \) in Equation 5 to find \( R \):
\[
R = \frac{4}{3} T = \frac{4}{3} \times 9 = 12
\]

Therefore, the ages of the three sisters are:
- Rhoda: \( R = 12 \) years
- Sally: \( S = 18 \) years
- Tabitha: \( T = 9 \) years

To summarize:
- Rhoda is 12 years old.
- Sally is 18 years old.
- Tabitha is 9 years old.