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Turkey's government requires at least a 
(2)/(3) majority of Parliament members to approve any constitutional changes. There are 550 seats in the Parliament. Of those, 313 of the seats are occupied by members who have pledged to support a particular constitutional change. Which inequality represents the number of additional Parliament members, 
m, who would need to support the constitutional change to achieve the required majority?
Choose 1 answer:
(A) 
m >= 53. bar(6)
(B) 
m >= 158
(C) 
m >= 303
(D) 
m >= 366. bar(6)

Turkey's government requires at least a 23 \frac{2}{3} majority of Parliament members to approve any constitutional changes. There are 550550 seats in the Parliament. Of those, 313313 of the seats are occupied by members who have pledged to support a particular constitutional change. Which inequality represents the number of additional Parliament members, m m , who would need to support the constitutional change to achieve the required majority?\newlineChoose 11 answer:\newline(A) m53.6 m \geq 53 . \overline{6} \newline(B) m158 m \geq 158 \newline(C) m303 m \geq 303 \newline(D) m366.6 m \geq 366 . \overline{6}

Full solution

Q. Turkey's government requires at least a 23 \frac{2}{3} majority of Parliament members to approve any constitutional changes. There are 550550 seats in the Parliament. Of those, 313313 of the seats are occupied by members who have pledged to support a particular constitutional change. Which inequality represents the number of additional Parliament members, m m , who would need to support the constitutional change to achieve the required majority?\newlineChoose 11 answer:\newline(A) m53.6 m \geq 53 . \overline{6} \newline(B) m158 m \geq 158 \newline(C) m303 m \geq 303 \newline(D) m366.6 m \geq 366 . \overline{6}
  1. Determine majority votes: Determine the number of votes needed for a 23\frac{2}{3} majority.\newlineA 23\frac{2}{3} majority means that more than two-thirds of the total number of seats must approve the constitutional change. To find this number, we multiply the total number of seats by 23\frac{2}{3}.\newlineCalculation: 23×550\frac{2}{3} \times 550\newline= 366.666366.666\ldots\newlineSince we need a whole number of seats and we can't have a fraction of a seat, we need to round up to the next whole number because a majority requires at least this number, not less.\newlineRounded up: 367367 seats needed for a 23\frac{2}{3} majority.
  2. Calculate number of seats needed: Determine the number of additional votes needed.\newlineWe know that 313313 seats are already pledged to support the change. To find out how many more are needed, we subtract the number of seats already pledged from the total number needed for a majority.\newlineCalculation: 367313367 - 313\newline=54= 54\newlineSo, 5454 additional members are needed to reach the required majority.

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