Last year a state senate consisting of only Republican and Democrat members had 20 more Republican members than Democrat members. This year the senate has the same number of members as last year, but it has 2 fewer Republican members than last year. If th : Crackverbal Support

Last year a state senate consisting of only Republican and Democrat members had 20 more Republican members than Democrat members. This year the senate has the same number of members as last year, but it has 2 fewer Republican members than l Print

Modified on: Tue, 12 Oct, 2021 at 12:31 PM

CONCEPT: The question tests on the abilities to frame and solve algebraic equations.

SOLUTIONS:

Let D = the number of Democrat senators last year

Then D + 20 = the number of Republican senators last year,

As the total members remain same;

The number of Democrat senators this year

=D+2 (These are the 2 Republican Members who turned Democratic)

Thus, the number of Republican senators this year

= Number of Republican senators last year + 2

(D + 20) - 2

= D + 18 (The two members have been moved from Republic to Democrat)

Total Senate Members this year

= Republic + Democrat

= (D+18) + (D+2) = 2D+20

Thus according to question,

(D + 18) [Republic Members this year]

= (2/3) (2D+20) [Total Senators this year]

3(D + 18) = 2(2D + 20)

3D + 54 = 4D + 40

14 = D

Therefore, the total number of senators this year is 2(14) + 20 = 48.(Option E)

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Last year a state senate consisting of only Republican and Democrat members had 20 more Republican members than Democrat members. This year the senate has the same number of members as last year, but it has 2 fewer Republican members than l Print

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