In a certain year, there were 92 female officials in Congress, which is comprised of the House of Representatives and the Senate

Question

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In a certain year, there were 92 female officials in Congress, which is comprised of the House of Representatives and the Senate

. If there were 64 more female members of the House of Representatives than female senators, find the number of females in each house of Congress.

Mathematics

1 answer:

crimeas [40] · Answer 1 · 2023-03-29T11:31:34+03:00

Answer:

There are 78 female members of the House of Representatives and 14 female members of the Senate.

Step-by-step explanation:

Let h equal the amount of female members of the House of Representatives and s equal the amount of female members in the Senate.

Since the amount of female officials in Congress is 92, and is made up of the House of Representatives and the Senate, we can represent this as the equation h+s=92

Since there are 64 more female members in the House of Representatives than female Senators, the senators would need 64 more female members to have the same amount as the House of Representatives. We can represent this as h=s+64.

Substituting, we get s+64+s=92, which simplifies to 2s+64=92. Subtracting 64 from both sides, we get 2s=28, which equals to s=14. There are 14 female senators. Substituting back into h+s=92, 14+s=92, and s=78. Therefore, there are 78 female members of the House of Representatives and 14 female members of the Senate.