Sat question (Answer is 6)

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

This problem would probably be solved quicker by using the answer choices, but it can be solved algebraically using a system of equations:

We find the average by dividing the sum by the number of objects. In this example, the sum was 120 and there were x members, so the average would be y yards each: 120/x = y

in the second scenario, two more members join, and each member gets 5 fewer yards. This can be written algebraically: 120/(x+2) = (y-5)

We can substitute the first equation in for y in the second equation: 120/(x+2) = 120/x - 5

To get rid of the denominators, multiply everything by the LCD which is x(x+2). That leaves us with: 120x = 120(x+2) -5(x)(x+2)

Simplify: 120x = 120x +240 -5x² -10x

Move everything over to the left side of the equal sign so it is equal to zero and can be factored: 5x² +10x -240 = 0

Factor out GCF of 5: 5(x² + 2x - 48) = 0

Factor trinomial: 5(x+8)(x-6) = 0

So x= -8 and 6. There can’t be a negative amount of yards, so that value is rejected and the only answer is x=6 yards.