The sum of the ages of a father and his son is 50 years. If the father is 30 yea

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Question: The sum of the ages of a father and his son is 50 years. If the father is 30 years older than the son, how old is the son?

Options:

Correct Answer: 20

Solution:

Let the son\'s age be x. Then the father\'s age is x + 30. So, x + (x + 30) = 50. Solving gives x = 10.

The sum of the ages of a father and his son is 50 years. If the father is 30 years older than the son, how old is the son?

The sum of the ages of a father and his son is 50 years. If the father is 30 years older than the son, how old is the son?

Correct Answer: 10

Step 1: Let the son's age be represented by the variable x.
Step 2: Since the father is 30 years older than the son, we can express the father's age as x + 30.
Step 3: According to the problem, the sum of the father's age and the son's age is 50 years. We can write this as an equation: x + (x + 30) = 50.
Step 4: Simplify the equation: Combine like terms to get 2x + 30 = 50.
Step 5: To isolate 2x, subtract 30 from both sides of the equation: 2x = 50 - 30, which simplifies to 2x = 20.
Step 6: Now, divide both sides by 2 to solve for x: x = 20 / 2, which gives x = 10.
Step 7: Therefore, the son's age is 10 years.

Algebraic Equations – The question tests the ability to set up and solve linear equations based on relationships between variables.
Word Problems – The question involves translating a real-world scenario into a mathematical equation.