Subjects algebra

Age Problem 2C474E

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1. **State the problem:** Nilopal is 2 years older than Devjan, who is 7 years older than John. Their combined age is 61 years. We need to find the age of each person. 2. **Define variables:** Let John's age be $x$ years. 3. **Express other ages in terms of $x$:** - Devjan's age = $x + 7$ - Nilopal's age = Devjan's age + 2 = $x + 7 + 2 = x + 9$ 4. **Write the equation for their combined age:** $$x + (x + 7) + (x + 9) = 61$$ 5. **Simplify the equation:** $$3x + 16 = 61$$ 6. **Isolate $x$:** $$3x = 61 - 16$$ $$3x = 45$$ 7. **Divide both sides by 3:** $$\cancel{3}x = \cancel{3}15$$ $$x = 15$$ 8. **Find each person's age:** - John = $15$ years - Devjan = $15 + 7 = 22$ years - Nilopal = $15 + 9 = 24$ years **Final answer:** John is 15 years old, Devjan is 22 years old, and Nilopal is 24 years old.