Question

to amend a country’s constitution, \\(\frac{5}{9}\\) of the 60 states in that country must approve the amendment. if 31 states approve an amendment, will the constitution be amended? the constitution will be amended \\(\frac{5}{9}\\) of the states means at least \\(\square\\) states must approve the amendment (type a whole number)

Explanation:

Step1: Calculate required states

To find the number of states required, multiply the total number of states (60) by the fraction $\frac{5}{9}$. So, $60\times\frac{5}{9}=\frac{300}{9}=\frac{100}{3}\approx33.33$.

Step2: Compare with approved states

We have 31 states that approved. Since $31 < 33.33$, we need to find the smallest whole number greater than or equal to $\frac{100}{3}$. $\frac{100}{3}\approx33.33$, so the least number of states required is 34 (because we can't have a fraction of a state, we round up to the next whole number). Wait, actually, the problem says "at least" how many states must approve. Wait, maybe I misread. Wait, the first part: To amend the constitution, $\frac{5}{9}$ of the 60 states must approve. So calculate $\frac{5}{9}\times60$. Let's do that again: $\frac{5\times60}{9}=\frac{300}{9}=\frac{100}{3}\approx33.33$. Since we need a whole number of states, and we need at least that fraction, we need to round up to the next whole number because 33 states would be $\frac{33}{60}=\frac{11}{20}=0.55$, and $\frac{5}{9}\approx0.555...$. So 33 is less than $\frac{100}{3}$, 34 is more. Wait, but the problem is: If 31 states approve, will the constitution be amended? Wait, no, the second part: "The constitution will be amended $\frac{5}{9}$ of the states means at least [ ] states must approve the amendment." Wait, maybe the first question is to find the number of states required, which is the ceiling of $\frac{5}{9}\times60$. Let's compute $\frac{5}{9}\times60 = \frac{300}{9} = 33.\overline{3}$. So we need at least 34 states? Wait, no, maybe the problem is: To amend the constitution, $\frac{5}{9}$ of the 60 states must approve. So calculate $\frac{5}{9} \times 60$. Let's do that: 60 divided by 9 is $\frac{20}{3}$, times 5 is $\frac{100}{3} \approx 33.33$. Since we can't have a fraction of a state, we need to round up to 34? Wait, but maybe the problem is asking for the minimum number of states, so we take the ceiling of $\frac{100}{3}$, which is 34. But wait, the user's question: "The constitution will be amended $\frac{5}{9}$ of the states means at least [ ] states must approve the amendment." So we need to find the smallest whole number $n$ such that $n \geq \frac{5}{9} \times 60$. So $\frac{5}{9} \times 60 = \frac{300}{9} = \frac{100}{3} \approx 33.33$. So $n$ must be 34? Wait, no, maybe I made a mistake. Wait, 33 states: $\frac{33}{60} = \frac{11}{20} = 0.55$, and $\frac{5}{9} \approx 0.555...$. So 33 is less than $\frac{5}{9}$ of 60, 34 is more. So the minimum number of states is 34. But wait, the problem says "Type a whole number". Let's check again: $\frac{5}{9} \times 60 = \frac{300}{9} = 33.\overline{3}$. So we need to round up to the next whole number, which is 34. So the answer is 34.

Answer:

34