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A boy is 30 years younger than this fath...

A boy is `30` years younger than this father. If the sum of the ages of the son and the father is `56`, find the age of the son.

A

`13` years

B

`12` years

C

`11` years

D

`10` years

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we can follow these instructions: ### Step 1: Define the variables Let the age of the father be represented by \( x \). Since the son is 30 years younger than the father, we can express the son's age as \( x - 30 \). ### Step 2: Set up the equation According to the problem, the sum of the ages of the son and the father is 56. We can write this as: \[ x + (x - 30) = 56 \] ### Step 3: Simplify the equation Now, simplify the left side of the equation: \[ x + x - 30 = 56 \] This simplifies to: \[ 2x - 30 = 56 \] ### Step 4: Solve for \( x \) Next, we will isolate \( x \) by adding 30 to both sides of the equation: \[ 2x - 30 + 30 = 56 + 30 \] This simplifies to: \[ 2x = 86 \] Now, divide both sides by 2: \[ x = \frac{86}{2} = 43 \] ### Step 5: Find the son's age Now that we have the father's age, we can find the son's age using the expression \( x - 30 \): \[ \text{Son's age} = 43 - 30 = 13 \] ### Final Answer The age of the son is **13 years**. ---
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