The annual salaries of a congressman and a senator total $288,900. If the senator makes $41,300 more than the congressman, how do you find each of their salaries?

Question

Nathan Axel · Accepted Answer

#color(green)("Salary of Senator " = $165,100#

#color(blue)("Salary of Congressman " = $123,800# Let the salary of a congressman as 'c' and that of a senator as 's'. #"Given " c + s = $288,900 " Eqn (1)# #"Also given " -c + s = $41,300 " Eqn (2)# Adding Eqns (1) & (2), #cancelc + s cancel(- c) + s = 288900 + 41300# #2 s = 330200 " or " s = 330200 / 2 = #165,100# #c = 288900 - s = 288900 - 165100 = $123,800#

Savannah Anderson · Answer

undefined Let's denote the congressman's salary as C and the senator's salary as S.

We have two equations:

1. S + C = 288,900 (the total annual salaries)
2. S = C + 41,300 (the senator's salary is $41,300 more than the congressman's salary)

We can use substitution or elimination to solve this system of equations.

Using substitution, we substitute the expression for S from equation 2 into equation 1:

C + (C + 41,300) = 288,900
2C + 41,300 = 288,900
2C = 288,900 - 41,300
2C = 247,600
C = 247,600 / 2
C = 123,800

Now, we can find S using the value of C:

S = C + 41,300
S = 123,800 + 41,300
S = 165,100

So, the congressman's salary is $123,800 and the senator's salary is $165,100.