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Two middle school classes take a vote on the destination for a class trip. Class A has 25 students, 56% of whom voted to go to St. Louis. Class B has n students, 60% of whom voted to go to St. Louis. If 57.5% of the two classes combined voted to go to St. Louis, what is the value of n

Respuesta :

Answer:

The value of n is 15.

Step-by-step explanation:

The combined proportion is computed using the formula:

[tex]P=\frac{n_{A}\cdot p_{A}+n_{B}\cdot p_{B}}{n_{A}+n_{B}}[/tex]

The information provided is as follows:

[tex]n_{A}=25\\p_{A}=0.56\\n_{B}=n\\p_{B}=0.60\\P=0.575[/tex]

Compute the value of n as follows:

[tex]P=\frac{n_{A}\cdot p_{A}+n_{B}\cdot p_{B}}{n_{A}+n_{B}}[/tex]

[tex]0.575=\frac{25\times 0.56+n\times 0.60}{25+n}\\\\0.575(25+n)=14+0.60n\\\\14.375+0.575n=14+0.60n\\\\0.60n-0.575n=14.375-14\\\\0.025n=0.375\\\\n=15[/tex]

Thus, the value of n is 15.

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