On a science test, Jake scored P points, Derek scored twice as many as Jake, and Sandy scored within 10 points of Derek. If Sandy scored S points, which of the following best describes Sandy's score?
I is absolute value
A. I S - 2P I = 10
B. I S - 2P I < or equal to 10
C. I S - P I < or equal to 10
D. I S - P I > or equal to 10
|x-a| is the distance from x to a
So, B
Well, let's see. Jake scored P points, Derek scored twice as many as Jake, so Derek scored 2P points. Now, Sandy scored within 10 points of Derek, which means her score, S, can be either greater than or less than Derek's score, 2P.
If we consider the case where Sandy's score is greater than Derek's, then we have S > 2P. Taking the absolute value of the difference between the two, we have |S - 2P|. Now, we need this to be less than or equal to 10, which can be written as |S - 2P| ≤ 10.
So, the best answer is B, I S - 2P I ≤ 10.
Let's break down the information given in the question.
Jake scored P points.
Derek scored twice as many points as Jake, so Derek scored 2P points.
Sandy scored within 10 points of Derek.
To describe Sandy's score using absolute value, we can say that I S - 2P I is less than or equal to 10, because Sandy's score could be 10 points less than Derek's, or it could be 10 points more than Derek's.
Therefore, the correct answer is B. I S - 2P I < or equal to 10.
To determine the relationship between Sandy's score (S) and Jake's score (P), we need to analyze the given information. Let's break it down step by step.
1. Jake's score: Jake scored P points.
2. Derek's score: Derek scored twice as many as Jake, which means Derek scored 2P points.
3. Sandy's score: Sandy scored within 10 points of Derek, so Sandy's score could be either 10 points higher or 10 points lower than Derek's score. Thus, Sandy's score can be represented as either 2P + 10 or 2P - 10.
Now, let's evaluate the answer options based on the relationships between Sandy's score (S) and Jake's score (P) using the information we derived above.
A. |S - 2P| = 10: This option allows Sandy's score to be exactly 10 points higher or lower than Derek's score but does not take into account Jake's score. It does not consider that Derek's score is twice Jake's score. Hence, option A is not the best description.
B. |S - 2P| ≤ 10: This option allows Sandy's score to be within 10 points of Derek's score, both higher or lower. It satisfies the condition that Sandy's score can be 10 points higher or 10 points lower than Derek's score. However, it does not take into account the relationship between Sandy's score and Jake's score. Therefore, option B is not the best description.
C. |S - P| ≤ 10: This option allows Sandy's score to be within 10 points of Jake's score, both higher or lower. Since Jake's score is P, this option considers the relationship between Sandy's score and Jake's score. Hence, option C is a possible best description.
D. |S - P| ≥ 10: This option states that the absolute difference between Sandy's score and Jake's score must be greater than or equal to 10. However, the given information does not support this condition. Option D is not the best description.
Therefore, the best description of Sandy's score is option C: |S - P| ≤ 10.