Questions: The amount y (in billions of dollars) of income taken in by a certain country's social security administration for old-age and survivor's insurance in year x can be approximated by the equation below. 110.9(x-2010)=9y-4375.48 Assuming the trend continues, find the year in which 794.22 billion dollars will be taken in. What is the value of y ? y=794.22 (Type an integer or a decimal. Do not include the symbol in your answer.) In the year , 794.22 billion dollars will be taken in.

Find the year \( x \) when \( y = 794.22 \) billion dollars will be taken in.

Substitute \( y = 794.22 \) into the equation.

The given equation is: \[ 110.9(x - 2010) = 9y - 4375.48 \] Substitute \( y = 794.22 \): \[ 110.9(x - 2010) = 9(794.22) - 4375.48 \]

Calculate the right-hand side of the equation.

\[ 9(794.22) = 7147.98 \] \[ 7147.98 - 4375.48 = 2772.5 \] So, the equation becomes: \[ 110.9(x - 2010) = 2772.5 \]

Solve for \( x \).

Divide both sides by \( 110.9 \): \[ x - 2010 = \frac{2772.5}{110.9} \] \[ x - 2010 = 25 \] Add \( 2010 \) to both sides: \[ x = 2010 + 25 \] \[ x = 2035 \]

The year is \( \boxed{2035} \).

The year in which 794.22 billion dollars will be taken in is \( \boxed{2035} \).