A and B are of different ages. If A is 5 years older than B and the sum of their

A and B are of different ages. If A is 5 years older than B and the sum of their ages is 45, what is A's age?

A and B are of different ages. If A is 5 years older than B and the sum of their ages is 45, what is A's age?

Correct Answer: 25

Step 1: Let B's age be represented by the variable x.
Step 2: Since A is 5 years older than B, we can express A's age as x + 5.
Step 3: The problem states that the sum of A's age and B's age is 45. We can write this as: x + (x + 5) = 45.
Step 4: Simplify the equation: Combine like terms to get 2x + 5 = 45.
Step 5: Subtract 5 from both sides of the equation: 2x = 40.
Step 6: Divide both sides by 2 to find x: x = 20. This means B is 20 years old.
Step 7: Now, to find A's age, substitute x back into the equation for A's age: A = x + 5 = 20 + 5.
Step 8: Calculate A's age: A = 25.

Algebraic Equations – The question tests the ability to set up and solve linear equations based on relationships between variables.
Age Problems – It specifically involves solving age-related problems, which often require translating verbal statements into mathematical expressions.