High School

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The number of questions Tyler answers correctly is within 2 of the number of Benjamin’s correct answers.

**Part A:** Write and solve an absolute value inequality to determine the number of questions Tyler answers correctly.

**Part B:** Based on your answer to Part A, what prizes will Tyler win? Explain.

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**Additional Information:**

Ms. Smith’s class will participate in an Algebra-Thon to raise money for a class trip. The Algebra-Thon workbook has 100 math problems. Students can raise money based on the number of math problems they answer correctly or by accepting a donation without regard to the number of math problems answered correctly. Benjamin, a student in the class, answers 80 math problems correctly. His grandmother pays $0.25 per correct answer. His uncle gives him a donation.

Answer :

Final answer:

Tyler's score can range between 78 and 82, based on the absolute value inequality representing the differential between his and Benjamin's scores. The available prize for Tyler cannot be determined based on the given information.

Explanation:

The problem is proposing an absolute value inequality regarding the number of questions Tyler and Benjamin answered correctly in the Algebra-Thon. In words, we could say that difference between the number of questions Benjamin and Tyler answered correctly can be at most 2. This sets up the absolute value inequality: |B - T| ≤ 2 where B represents the number of problems Benjamin answers correctly and T represents the number of problems Tyler answers correctly.

Here, given Benjamin answered 80 problems correctly, we substitute B with 80 to obtain |80 - T| ≤ 2. Solving this absolute value inequality, we get 78 ≤ T ≤ 82. This means Tyler could have answered correctly anywhere between 78 to 82 math problems inclusive.

For Part B, the solution does not provide information about what prizes are offered in the Algebra-Thon based on the number of questions answered correctly. More information would be needed to determine what prizes, if any, Tyler would win.

Learn more about Absolute Value Inequality here:

https://brainly.com/question/32844662

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Final answer:

The number of questions Tyler answers correctly can be represented by the absolute value inequality |T - 80| ≤ 2. Solving for T, we get 78 ≤ T ≤ 82. Depending on the rewards offered, Tyler could earn from $19.50 to $20.50 if the rate is $0.25 per correct answer.

Explanation:

For Part A, the relationship between the number of correct answers for Tyler and Benjamin can be represented by the absolute value inequality |T - 80| ≤ 2 where T represents the number of questions that Tyler answers correctly. This inequality represents the fact that the number of questions Tyler answers correctly is within two of the number Benjamin answered correctly, which is 80. Solving this inequality we get 78 ≤ T ≤ 82. So Tyler can answer from 78 to 82 questions correctly.

For Part B, the prizes Tyler could win depends on the specifics provided by the teacher or the Algebra-Thon workbook, which is not provided in this question. However, following Benjamin's scenario, if Tyler also got $0.25 per correct answer, he would earn from $19.50 to $20.50.

Learn more about Absolute Value Inequality here:

https://brainly.com/question/33786594

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