State defining any unknown quantities, solve problem, showing all work

Question

If there are 535 members of congress and 45 more republicians than democrats, how many of each party are there, assuming that there is no independents?

Answer 1

Let R = the number of Republicans and D = the number of Democrats.

• there are 535 members of congress: R + D = 535
• there are 45 more republicans than democrats: R = D + 45

 

     R + D = 535

     R = D + 45

 

Substitute D+45 in place of R in the first equation:

 

     R + D = 535

     D + 45 + D = 535

     2D + 45 = 535

     2D = 490

     D = 245

 

     R = D + 45 = 245 + 45 = 290

 

Check:

     R + D = 535

     245 + 290 = 535

     535 = 535

     Check!