A man is 10 years older than his wife. If the sum of their ages is 70 years, how

A man is 10 years older than his wife. If the sum of their ages is 70 years, how old is the wife?

A man is 10 years older than his wife. If the sum of their ages is 70 years, how old is the wife?

Correct Answer: 30

Step 1: Let the wife's age be represented by the variable x.
Step 2: Since the man is 10 years older than his wife, we can express the man's age as x + 10.
Step 3: According to the problem, the sum of their ages is 70 years. We can write this as an equation: x + (x + 10) = 70.
Step 4: Simplify the equation: Combine like terms to get 2x + 10 = 70.
Step 5: To isolate 2x, subtract 10 from both sides of the equation: 2x = 70 - 10, which simplifies to 2x = 60.
Step 6: Now, divide both sides by 2 to find x: x = 60 / 2, which gives x = 30.
Step 7: Therefore, the wife's age is 30 years.

Algebraic Equations – The question tests the ability to set up and solve a linear equation based on relationships between variables.
Age Problems – The question involves understanding how to express age relationships and solve for unknowns.