Video: Writing and Evaluating Quotients of Rational Numbers Describing Real World Contexts

Jennifer is playing a game where she starts with 50 points and each incorrect move changes her score by the same amount. She made 7 incorrect moves, and lost 21 points. Which of the following expressions matches this situation? [A] −21/7 [B] −21 × 7 [C] 21/7 [D] 7/21 [E] −7/21. Evaluate the expression to find a number that represents the change in score after 1 incorrect move.

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Video Transcript

Jennifer is playing a game where she starts with 50 points and each incorrect move changes her score by the same amount. She made seven incorrect moves, and lost 21 points. Which of the following expressions matches this situation? Is it A) negative 21 divided by seven, B) negative 21 multiplied by seven, C) 21 divided by seven, D) seven divided by 21, or E) negative seven divided by 21? Evaluate the expression to find a number that represents the change in score after one incorrect move.

We are told in the question that Jennifer makes seven incorrect moves and loses 21 points. As she is losing points, our answer must be negative, which rules out option C and D. In order to find the expression that represents the change in score after one incorrect move, we need to divide the total points change by the number of incorrect moves.

The total points change was negative 21. And the number of incorrect moves was seven. This means that the correct expression that matches the situation is option A, negative 21 divided by seven. 21 divided by seven is equal to three. Therefore, negative 21 divided by seven is equal to negative three. Dividing a negative number by a positive number gives a negative answer. For each incorrect move that Jennifer makes, she loses three points. Her change in score after one incorrect move is negative three.

Whilst we’re not asked to in this particular question, we could calculate Jennifer’s new score by subtracting 21 from 50. She started with 50 points and lost 21 points due to seven incorrect moves. 50 minus 21 is equal to 29. This means that Jennifer’s new score, after these seven incorrect moves, is 29.

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