Working as an insurance salesman, Brian makes a base wage of \( \$ 46000 \) plus a commission of \( \$ 60 \) on every policy he sells. a) If \( I \) represents his yearly income and \( n \) represents the number of policies he sells in a year, write an equation that relates his income in terms on the number of policies he sells. b) Use the equation to determine Brian's income if he sells 168 policies. c) Use the equation to determine how many policies Brian needs to sell to have an income of \( \$ 55000 \). .

a) To express Brian's yearly income \( I \) in terms of the number of policies \( n \) he sells, we can write the equation as follows: \[ I = 46000 + 60n \] Here, \( 46000 \) is his base wage, and \( 60n \) represents the commission he earns from selling \( n \) policies. b) To determine Brian's income if he sells 168 policies, we can substitute \( n = 168 \) into the equation: \[ I = 46000 + 60(168) \] Calculating the commission: \[ 60 \times 168 = 10080 \] Now, substituting this back into the equation: \[ I = 46000 + 10080 = 56080 \] So, if Brian sells 168 policies, his income will be \( \$ 56080 \). c) To find out how many policies Brian needs to sell to have an income of \( \$ 55000 \), we set \( I = 55000 \) in the equation and solve for \( n \): \[ 55000 = 46000 + 60n \] Subtract \( 46000 \) from both sides: \[ 55000 - 46000 = 60n \] \[ 9000 = 60n \] Now, divide both sides by \( 60 \): \[ n = \frac{9000}{60} = 150 \] Thus, Brian needs to sell **150 policies** to have an income of \( \$ 55000 \).