Subjects algebra

Joy Leo Ages

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Joy Leo Ages


1. **State the problem:** Joy is 9 years older than Leo. Three years ago, the sum of their ages was 29. We need to find Joy's current age. 2. **Define variables:** Let $L$ be Leo's current age. Since Joy is 9 years older, Joy's age is $J = L + 9$. 3. **Express the condition from three years ago:** Three years ago, Leo's age was $L - 3$, and Joy's age was $J - 3 = L + 9 - 3 = L + 6$. The sum of their ages then was $29$, so: $$ (L - 3) + (L + 6) = 29 $$ 4. **Solve the equation:** Combine like terms: $$ 2L + 3 = 29 $$ Subtract 3 from both sides: $$ 2L = 26 $$ Divide both sides by 2: $$ L = 13 $$ 5. **Find Joy's current age:** Recall $J = L + 9$, so: $$ J = 13 + 9 = 22 $$ **Final answer:** Joy is currently 22 years old.