Question

An after-school sewing club has 120 yards of fabric to divide equally among the members of the club. When two more students join the club at the last minute, each member gets 5 fewer yards of fabric to work with. How many members were in the club before the two additional students joined

Answer 1

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, $\frac{120}{x} =y$ -------(1)

In the second scenario, two more members join, and each member gets 5 fewer yards.

This can be written algebraically: $\frac{120}{x+2} =y-5$ -------(2)

We can substitute the first equation for y in the second equation: $\frac{120}{x+2}=\frac{120}{x}-5$

⇒$\frac{120}{x+2} =\frac{120-5x}{x}$

⇒$120x=120x+240-5x^{2} -10x$

⇒$5x^{2} +10x-240=0$

⇒$x^{2} +2x-48=0$

⇒$x^{2} +8x-6x-48=0$

⇒$x(x+8)-6(x+8)=0$

⇒$(x+8)(x-6)$

⇒$x=-8, x=6$

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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Answer 2

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.

How to calculate how many members there were?

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.

• 120 ÷ 6 = 20 yards.

Now, knowing that 2 more members joined, we must divide 120 by 8 to check the information in the statement.

• 120 ÷ 8 = 15

According to the above, the number of members at the beginning was 6.

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