Question

The Texas State Legislation is comprised of state senators and state

representatives. There is a greater number of representatives than
senators. The sum of the number of representatives and the number of
senators is 181. The difference of the number of representatives and
number of senators 119.
a. Write a system of equations to find the number of state representatives,
r, and senators, s.
b. How many senators and how many representatives make up the Texas
State Legislature?

Answer 1

I. r = 150 state representatives.

II. s = 31 senators.

Explanation:

Let the number of state representatives, be r

Let the number of senators be s.

a. The system of equations are given by translating the word problem into an algebraic expression, we have;

r + s = 181 ...... equation 1

r - s = 119 ...... equation 2

b. To find the values;

First of all, let's find the number of senators by using the substitution method.

From equation 1;

r = 181 - s ...... equation 3

Substituting eqn 3 into eqn 2;

181 - s - s = 119

181 - 2s = 119

181 - 119 = 2s

2s = 62

s = 62/2

s = 31 senators.

To find the value of r;

From equation 3;

r = 181 - s

r = 181 - 31

r = 150 state representatives.