Maths question (Faction)

Question

there were 3/4 as many girls as boys in the science club. after 21 boys left to join another club, there were 3 times as many girls as boys in the science club. how many pupils were there in the science club at first?

Answer 1

Let's set up some equations. We have the variables of the number girls in the club, which we'll call G, and the variable of the number of boys in the club before some of them left, which we'll call B. In the original club, there were 3/4 as many girls as boys, so G = 3/4B.

After 21 boys left, which can be represented by (B - 21), there were 3 times as many girls as boys in the science club. We can represent this with the equation G = 3(B - 21).

Now we have our two equations, so we can solve for B! G = 3/4B from our first equation, so we substitute that in the left side of our second equation to get 3/4B = 3(B - 21).

Simplifying (which can be done different ways), divide both sides by three and you get 3/12B = B - 21. Add 21 to both sides and you get 3/12B + 21 = B. Subtract 3/12 B from both sides and you get 21 = 9/12 B. 9/12 = 3/4, so 21 = 3/4 B. Divide both sides by 3/4 (i.e. multiply both sides by 4/3) and you get B = 28. This is the number of boys in the club at first.

Now, we solve for G. G = 3/4B, so G = 3/4 * 28, or G = 21. The total pupils in the class at first is B + G, or 28 + 21 so your answer is 49!