A ranking of football teams uses
the formula 𝑆 is equal to 𝑊 over 𝑊 plus 𝐿 to calculate the relative scores, 𝑆,
of the teams based on the number of games they won, 𝑊, and the number of games they
lost, 𝐿. Which of the following expresses
the number of games won in terms of the other variables? Is it A) 𝑊 equals 𝑆𝐿 over 𝑆
minus one, B) 𝑊 equals 𝐿 over 𝑆 minus one, C) 𝑊 equals 𝑆𝐿 over one minus 𝑆,
or D) 𝑊 equals 𝐿 over one minus 𝑆?
In order to answer this question,
we need to rearrange the formula 𝑆 equals 𝑊 over 𝑊 plus 𝐿 to make 𝑊 the
subject. Our first step is to multiply both
sides of the formula by 𝑊 plus 𝐿. On the left-hand side, this leaves
us with 𝑆 multiplied by 𝑊 plus 𝐿. On the right-hand side, the 𝑊 plus
𝐿s cancel, leaving us with 𝑊.
Our next step is to distribute the
parenthesis. We need to multiply 𝑆 by 𝑊 and 𝑆
by 𝐿. 𝑆 multiplied by 𝑊 is 𝑆𝑊, and 𝑆
multiplied by 𝐿 is 𝑆𝐿. We now have 𝑆𝑊 plus 𝑆𝐿 is equal
to 𝑊. As we are trying to make 𝑊 the
subject, we need to get all the terms with 𝑊 in them on one side. In order to do this, we can
subtract 𝑆𝑊 from both sides of the equation. This leaves us with 𝑆𝐿 is equal
to 𝑊 minus 𝑆𝑊.
Both terms on the right-hand side
have a 𝑊 in them. This means that we can factorise
this out. Factorising out the 𝑊 gives us 𝑊
multiplied by one minus 𝑆. This is because 𝑊 multiplied by
one is equal to 𝑊 and 𝑊 multiplied by negative 𝑆 is equal to negative 𝑆𝑊.
Our final step is to divide both
sides of the equation by one minus 𝑆. On the right-hand side, the one
minus 𝑆 terms cancel. This leaves us with 𝑊 is equal to
𝑆𝐿 over one minus 𝑆. The correct answer was option C 𝑊
is equal to 𝑆𝐿 over one minus 𝑆. This is the formula that expresses
the number of games won in terms of the other variables, 𝑆 and 𝐿.