Question

There are 435 representatives and 100

senators serving in the United States Congress .how many identical groups with the same numbers of representatives and senators can be formed from all of Congress if we want to largest group is possible?How many representatives and senators would be in each group?

Answer 1

Answer: There are 5 identical groups with the same numbers of representatives and senators that can be formed.

There are 87 representatives in each group and 20 senators in each group.

Explanation:

Since we have given that

Number of representatives = 435

Number of senators serving in the United States Congress = 100

Now, we need to find the number of identical groups with the same numbers of representatives and senators that can be formed from all of Congress if we want to form largest group,

For largest group, we'll do H.C.F. of 435 and 100,

So,

`H.C.F.\ of\ 435\ and\ 100=5`

So, there are 5 identical groups with the same numbers of representatives and senators that can be formed.

Now, Number of representatives in each group is given by

`(435)/(5)=87`

Number of senators in each group is given by

`(100)/(5)=20`

Hence, there are 87 representatives in each group and 20 senators in each group.

Answer 2

Answer: The number of representatives and senators can be formed from all of Congress if we want to largest group is possible =5

The number of representatives and senators would be 87 and 20 respectively in each group.

Explanation:

Given : There are 435 representatives and 100 senators serving in the United States Congress .

To find the largest possible group with same numbers of representatives and senators can be formed from all of Congress, we need to find GCF (Greatest Common Factor) of 435 and 100.

Prime factorization of 435 and 100 :-

`435 =29*5*3\\\\=100=2*2*5*5`

We can see that, GCF (435,100)=5

∴ The number of representatives and senators can be formed from all of Congress if we want to largest group is possible = 5

Now, the number of representatives in each group =
`(435)/(5)=87`

The number of senators in each group =
`(100)/(5)=20`