CPM Homework Help : AC Problem 7-98

In the spring of 2005, there were $30$ more Republicans than Democrats in the United States House of Representatives. There was also one member from an Independent Party. If there were $435$ representatives in all, how many Republicans were there? Write and solve an equation (or a system of equations) to find your solution.

Hint 1:

Write an equation for the problem. $x + \left(x − 30\right) + 1 = 435$

$x = \text{the number of Republicans}$

Hint 2:

Add like terms and solve for $x$ to find the number of Republicans.
$\begin{aligned}[t] 2x - 29 = 435\\ 2x = 464 \\x = 232 \end{aligned}$

Answer:

There were $232$ Republicans in the United States House of Representatives.