Halima is n years old. Her brother's age is 5 years more than half of her age. How old is her brother?

Analyze the question Halima's age is n. Her brother's age is "5 years more than half of her age." We need an algebraic expression for the brother's age.

Concept Translate the words into algebra:

• "Half of her age" means n/2
• "5 years more than" something means add 5 to it

Solution

1. Half of Halima's age = n/2
2. 5 years more than this = n/2 + 5

So the brother's age = n/2 + 5

Checking the options

• A. n/2 + 5/2 adds only 2.5, not 5, so it is wrong.
• B. n/2 − 5 subtracts 5, which would mean "5 years less than", so it is wrong.
• C. 5 − n/2 is the wrong order and the wrong operation, so it is wrong.
• D. n/2 + 5 matches our expression, so it is correct.

Quick check with a number: If Halima is 12, half of her age is 6, and 5 more is 11. Option D gives 12/2 + 5 = 11, which is correct.

Exam tip: In word problems, "more than" or "added to" means +, and "less than" or "reduced by" means −. Also, "5 more than X" is written X + 5, so the word "than" tells you what to start from.