Subjects algebra

Age Word Problems

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **Problem:** Mila is 4 years older than her brother Nelo. The sum of their present ages is 28. Step 1: Let Nelo's age be $x$. Then Mila's age is $x + 4$. Step 2: The sum of their ages is given as: $$x + (x + 4) = 28$$ Step 3: Simplify the equation: $$2x + 4 = 28$$ Step 4: Subtract 4 from both sides: $$2x = 24$$ Step 5: Divide both sides by 2: $$x = 12$$ Step 6: Nelo is 12 years old, Mila is $12 + 4 = 16$ years old. --- 2. **Problem:** Four years ago, Jenny was twice as old as her sister Ella. Jenny is now 20 years old. Find Ella's current age. Step 1: Let Ella's current age be $y$. Step 2: Four years ago, Jenny's age was $20 - 4 = 16$. Step 3: Four years ago, Ella's age was $y - 4$. Step 4: According to the problem: $$16 = 2(y - 4)$$ Step 5: Simplify: $$16 = 2y - 8$$ Step 6: Add 8 to both sides: $$24 = 2y$$ Step 7: Divide both sides by 2: $$y = 12$$ Step 8: Ella is currently 12 years old. --- 3. **Problem:** In 6 years, the sum of the ages of Carlo and his father will be 60. The father is now 35 years old. Find Carlo's current age. Step 1: Let Carlo's current age be $c$. Step 2: In 6 years, Carlo's age will be $c + 6$ and his father's age will be $35 + 6 = 41$. Step 3: The sum of their ages in 6 years is: $$ (c + 6) + 41 = 60 $$ Step 4: Simplify: $$ c + 47 = 60 $$ Step 5: Subtract 47 from both sides: $$ c = 13 $$ Step 6: Carlo is currently 13 years old. --- 4. **Problem:** Three years ago, Ana’s age was half of her mother’s age. Ana is now 15 years old. Find her mother's current age. Step 1: Let mother's current age be $m$. Step 2: Ana's age 3 years ago was $15 - 3 = 12$. Step 3: Mother's age 3 years ago was $m - 3$. Step 4: According to the problem: $$12 = \frac{1}{2}(m - 3)$$ Step 5: Multiply both sides by 2: $$24 = m - 3$$ Step 6: Add 3 to both sides: $$m = 27$$ Step 7: Ana's mother is currently 27 years old. --- 5. **Problem:** In 8 years, Mia will be 3 times as old as her brother. Her brother is now 10 years old. Find Mia's current age. Step 1: Let Mia's current age be $M$. Step 2: In 8 years, Mia's age will be $M + 8$ and her brother's age will be $10 + 8 = 18$. Step 3: According to the problem: $$M + 8 = 3 \times 18$$ Step 4: Simplify: $$M + 8 = 54$$ Step 5: Subtract 8 from both sides: $$M = 46$$ Step 6: Mia is currently 46 years old. --- **Final answers:** 1. Mila: 16 years, Nelo: 12 years 2. Ella: 12 years 3. Carlo: 13 years 4. Ana's mother: 27 years 5. Mia: 46 years