Members in the Spanish Club are \(20\) .
What is average (arithmetic mean) ?
Average (arithmetic mean) or arithmetic average, or simply just the mean or the average, is the sum of a collection of numbers divided by the count of numbers in the collection.
Average \(= \frac{Sum \ of \ all \ numbers}{Total \ numbers}\)
We have,
Let Members in the Spanish Club \(=x\)
Let Members in the French Club\(=z=30\)
Let Total number of students \(=y=x+z\)
The average weight of the students in the French Club is \(150\) pounds .
The average weight of the students in the Spanish Club is \(130\) pounds .
The average weight of all the students is \(142\) pounds .
So,
Average \(= \frac{Sum \ of \ all \ numbers}{Total \ numbers}\)
Average weight of students in the French Club \(= \frac{Sum \ of \ weights}{Total \ numbers \ of \ student}\)\(150=\frac{Sum \ of \ weights}{30}\)
Sum of weights \(=4500\)
The average weight of all the students = Average weight of students in (French Club + Spanish Club)
so,
\(142(x+z)=150*z+130*x\)
\(142(30+x)=150*30+130x\)
\(4260+142x=4500+130x\)
\(12x=240\)
\(x=20\)
So, Members in the Spanish Club are \(20\) .
Hence, we can say that the members in the Spanish Club are \(20\) .
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