If twice the age of the son is added of the father, the sum is 56 but if twice the age of the father is added to the age of son, the sum is 82 what is the age of the father

Answer 1

Let the age of the son be \( s \) and the age of the father be \( f \).

We can set up the following equations based on the information given:

1. \( 2s + f = 56 \) (twice the age of the son added to the father's age is 56)
2. \( 2f + s = 82 \) (twice the age of the father added to the son's age is 82)

Now, we can solve these two equations step by step.

From the first equation, we can express \( f \) in terms of \( s \):

\[ f = 56 - 2s \tag{1} \]

Now, substitute equation (1) into the second equation:

\[ 2(56 - 2s) + s = 82 \]

Expanding this, we get:

\[ 112 - 4s + s = 82 \]

Combining like terms:

\[ 112 - 3s = 82 \]

Now, subtract 112 from both sides:

\[ -3s = 82 - 112 \] \[ -3s = -30 \]

Dividing both sides by -3 gives:

\[ s = 10 \]

Now that we have the son's age, we can substitute \( s \) back into equation (1) to find the father's age:

\[ f = 56 - 2(10) \] \[ f = 56 - 20 \] \[ f = 36 \]

Thus, the age of the father is \( \boxed{36} \).