Members in the Spanish Club are [tex]20[/tex] .
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 [tex]= \frac{Sum \ of \ all \ numbers}{Total \ numbers}[/tex]
We have,
Let Members in the Spanish Club [tex]=x[/tex]
Let Members in the French Club[tex]=z=30[/tex]
Let Total number of students [tex]=y=x+z[/tex]
The average weight of the students in the French Club is [tex]150[/tex] pounds .
The average weight of the students in the Spanish Club is [tex]130[/tex] pounds .
The average weight of all the students is [tex]142[/tex] pounds .
So,
Average [tex]= \frac{Sum \ of \ all \ numbers}{Total \ numbers}[/tex]
Average weight of students in the French Club [tex]= \frac{Sum \ of \ weights}{Total \ numbers \ of \ student}[/tex][tex]150=\frac{Sum \ of \ weights}{30}[/tex]
Sum of weights [tex]=4500[/tex]
The average weight of all the students = Average weight of students in (French Club + Spanish Club)
so,
[tex]142(x+z)=150*z+130*x[/tex]
[tex]142(30+x)=150*30+130x[/tex]
[tex]4260+142x=4500+130x[/tex]
[tex]12x=240[/tex]
[tex]x=20[/tex]
So, Members in the Spanish Club are [tex]20[/tex] .
Hence, we can say that the members in the Spanish Club are [tex]20[/tex] .
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