Question

The number of representatives is 160 less than five times the number of senators. There are a total of 560 members. Find the number of senators and the number of representatives

Answer 1

The number of Senators are 120 and number of Representatives are 440.

Explanation:

Given,

Total number of members = 560

Solution,

Let the number of Senators be 'x'.

Since, the number of representatives is 160 less than five times the number of senators.

Framing the above sentence in equation form,we get the number of Representative.

So, number of Representative =
`5x-160`

Now, Total number of members is the sum of total number of Senators and total number of representative.

Total number of members = Total number of Senators + Total number of representative

On substituting the values, we get;

`x+5x-160=560\\\\6x=560+160\\\\6x=720\\\\x=(720)/(6)\\\\x=120`

Total number of Senators = 120

So, number of Representative =
`5*120-160=600-160=440`

Thus the number of Senators are 120 and number of Representatives are 440.