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In a certain town in Connecticut, the ratio of NY Yankees fans to
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12 Jan 2026, 09:12
12 Jan 2026, 09:12
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In a certain town in Connecticut, the ratio of NY Yankees fans to NY Mets fans is $3: 2$, and the ratio of NY Mets fans to Boston Red Sox fans is $4: 5$. If there are 300 baseball fans in the town, each of whom is a fan of exactly one of those three teams, how many NY Mets fans are there in this town?
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- Part of the project: GRE Daily Quant Challenge - Topic-Wise 2025!!!
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Re: In a certain town in Connecticut, the ratio of NY Yankees fans to
[#permalink]
31 Jan 2026, 12:57
31 Jan 2026, 12:57
Expert Reply
1. Combine the Ratios
We are given two separate ratios:
- Yankees (Y) to Mets (M): $3: 2$
- Mets (M) to Red Sox (R): 4 : 5
To combine them, the "Mets" part of the ratio must be the same number in both sets. The least common multiple (LCM) of 2 and 4 is 4 .
- Adjust the first ratio: Multiply both parts of $3: 2$ by 2 to get $6: 4$.
- Keep the second ratio: $4: 5$.
Now we have a single continuous ratio: Yankees : Mets : Red Sox $\(=6: 4: 5\)$
2. Find the Value of One "Part"
The total number of fans is 300 . We can represent the number of fans for each team as $\(6 x, 4 x\)$, and $5 x$ :
$$
\(\begin{gathered}
6 x+4 x+5 x=300 \\
15 x=300 \\
x=\frac{300}{15}=20
\end{gathered}\)
$$
Each "part" in our ratio represents 20 people.
3. Calculate the Number of Mets Fans
The ratio for Mets fans is $\(\mathbf{4}\)$ parts ( $\(4 x\)$ ):
$$
\(4 \times 20=80\)
$$
We are given two separate ratios:
- Yankees (Y) to Mets (M): $3: 2$
- Mets (M) to Red Sox (R): 4 : 5
To combine them, the "Mets" part of the ratio must be the same number in both sets. The least common multiple (LCM) of 2 and 4 is 4 .
- Adjust the first ratio: Multiply both parts of $3: 2$ by 2 to get $6: 4$.
- Keep the second ratio: $4: 5$.
Now we have a single continuous ratio: Yankees : Mets : Red Sox $\(=6: 4: 5\)$
2. Find the Value of One "Part"
The total number of fans is 300 . We can represent the number of fans for each team as $\(6 x, 4 x\)$, and $5 x$ :
$$
\(\begin{gathered}
6 x+4 x+5 x=300 \\
15 x=300 \\
x=\frac{300}{15}=20
\end{gathered}\)
$$
Each "part" in our ratio represents 20 people.
3. Calculate the Number of Mets Fans
The ratio for Mets fans is $\(\mathbf{4}\)$ parts ( $\(4 x\)$ ):
$$
\(4 \times 20=80\)
$$
gmatclubot
Re: In a certain town in Connecticut, the ratio of NY Yankees fans to [#permalink]
31 Jan 2026, 12:57
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