The number of members before the entry of two new participants was 6, because before they had 20 yards and after their entry each one had 15 yards.
To figure out how many members there were, we must try different numbers until we find which number matches the information. In this case, it can be affirmed that there were 6 members, that is to say that each one had 20 yards.
Now, knowing that 2 more members joined, we must divide 120 by 8 to check the information in the statement.
According to the above, the number of members at the beginning was 6.
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6 members were in the club before the two additional students joined.
Given that, the total fabric=120 yards.
Let x be the number of people and y be the average fabric each student gets.
Now, [tex]\frac{120}{x} =y[/tex] -------(1)
In the second scenario, two more members join, and each member gets 5 fewer yards.
This can be written algebraically: [tex]\frac{120}{x+2} =y-5[/tex] -------(2)
We can substitute the first equation for y in the second equation: [tex]\frac{120}{x+2}=\frac{120}{x}-5[/tex]
⇒[tex]\frac{120}{x+2} =\frac{120-5x}{x}[/tex]
⇒[tex]120x=120x+240-5x^{2} -10x[/tex]
⇒[tex]5x^{2} +10x-240=0[/tex]
⇒[tex]x^{2} +2x-48=0[/tex]
⇒[tex]x^{2} +8x-6x-48=0[/tex]
⇒[tex]x(x+8)-6(x+8)=0[/tex]
⇒[tex](x+8)(x-6)[/tex]
⇒[tex]x=-8, x=6[/tex]
There can’t be a negative amount of yards so that x=6 yards.
Hence, 6 members were in the club before the two additional students joined.
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