Question

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

Answer 1

Answer:

The value of n is 15.

Step-by-step explanation:

The combined proportion is computed using the formula:

$P=\frac{n_{A}\cdot p_{A}+n_{B}\cdot p_{B}}{n_{A}+n_{B}}$

The information provided is as follows:

$n_{A}=25\\p_{A}=0.56\\n_{B}=n\\p_{B}=0.60\\P=0.575$

Compute the value of n as follows:

$P=\frac{n_{A}\cdot p_{A}+n_{B}\cdot p_{B}}{n_{A}+n_{B}}$

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

Thus, the value of n is 15.