Video: SAT Practice Test 1 • Section 3 • Question 10

A ranking of football teams uses the formula 𝑆 = 𝑊/(𝑊 + 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? [A] 𝑊 = 𝑆𝐿/(𝑆 − 1) [B] 𝑊 = 𝐿/(𝑆 − 1) [C] 𝑊 = 𝑆𝐿/(1 − 𝑆) [D] 𝑊 = 𝐿/(1 − 𝑆)

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Video Transcript

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.

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