Question

1. rons age is two - thirds of marks age. marks age is three - fifths of saras age. sara is 9 years older than ron. how old is mark?

Explanation:

Step1: Define Variables

Let \( R \) be Ron's age, \( M \) be Mark's age, and \( S \) be Sara's age.

Step2: Translate Relationships to Equations

From "Ron’s age is two - thirds of Mark’s age", we have \( R=\frac{2}{3}M \).
From "Mark’s age is three - fifths of Sara’s age", we have \( M = \frac{3}{5}S\), which can be rewritten as \( S=\frac{5}{3}M \).
From "Sara is 9 years older than Ron", we have \( S=R + 9 \).

Step3: Substitute \( R \) and \( S \) in Terms of \( M \) into the Third Equation

Substitute \( R=\frac{2}{3}M \) and \( S=\frac{5}{3}M \) into \( S=R + 9 \):
\(\frac{5}{3}M=\frac{2}{3}M+9\)

Step4: Solve for \( M \)

Subtract \(\frac{2}{3}M\) from both sides:
\(\frac{5}{3}M-\frac{2}{3}M=\frac{2}{3}M + 9-\frac{2}{3}M\)
\(\frac{5M - 2M}{3}=9\)
\(\frac{3M}{3}=9\)
\(M = 9\)

Answer:

Mark is 9 years old.