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A cereal box is 2 inches wide. The height of the box is 3 inches more than the length. The volume is 216 in³, how tall is the box?

A cereal box is 2 inches wide. The height of the box is 3 inches more than the length. The volume is 216 in³, how tall is the box?

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Educational Math Problems and Concepts #### 1. Cereal Box Dimensions - **Problem:** A cereal box is 2 inches wide. The height of the box is 3 inches more than the length. The volume is 216 cubic inches. How tall is the box? - **Concepts Involved:** Volume of a rectangular prism, algebraic equations. #### 2. Flower Garden Perimeter - **Problem:** Martin has a flower garden that is 20 feet long and 15 feet wide. He wants to put a uniform walk around the garden and increase the area by 74 square feet. Find the width of the walk. - **Concepts Involved:** Area calculation, algebra. #### 3. Computer Usage Fee - **Problem:** To use a computer for color print formatting, the cost is $4 to log on plus an additional fee for every quarter-hour of use. It costs $14 to use the computer for one and a quarter hours. Determine the value of the additional fee per quarter-hour. - **Concepts Involved:** Linear equations, cost analysis. #### 4. Bouncing Ball Height - **Problem:** A ball is dropped from a height of 4 meters. After each bounce, it rises to 69% of its previous height. What height does the ball reach after 6 bounces? - **Concepts Involved:** Exponential decay, sequences and series. #### 5. Average Driving Speed - **Problem:** Troy's family traveled 360 miles. They drove 120 miles in the first 2 hours and then stopped for an hour to eat. If the entire trip, including the stop, took seven hours, what was their average driving speed? - **Concepts Involved:** Average speed calculation, distance and time relationships. #### Identifying Function Types - **Task:** Match the given problems to their corresponding function types. 1. **Linear** 2. **Quadratic** 3. **Rational** 4. **Radical** 5. **Exponential** Both the problems and the function types provided align closely with key mathematical concepts often discussed in middle and high school mathematics courses. Understanding these foundational problems and their solutions helps in grasping more complex mathematical principles.
Transcribed Image Text:### Educational Math Problems and Concepts #### 1. Cereal Box Dimensions - **Problem:** A cereal box is 2 inches wide. The height of the box is 3 inches more than the length. The volume is 216 cubic inches. How tall is the box? - **Concepts Involved:** Volume of a rectangular prism, algebraic equations. #### 2. Flower Garden Perimeter - **Problem:** Martin has a flower garden that is 20 feet long and 15 feet wide. He wants to put a uniform walk around the garden and increase the area by 74 square feet. Find the width of the walk. - **Concepts Involved:** Area calculation, algebra. #### 3. Computer Usage Fee - **Problem:** To use a computer for color print formatting, the cost is $4 to log on plus an additional fee for every quarter-hour of use. It costs $14 to use the computer for one and a quarter hours. Determine the value of the additional fee per quarter-hour. - **Concepts Involved:** Linear equations, cost analysis. #### 4. Bouncing Ball Height - **Problem:** A ball is dropped from a height of 4 meters. After each bounce, it rises to 69% of its previous height. What height does the ball reach after 6 bounces? - **Concepts Involved:** Exponential decay, sequences and series. #### 5. Average Driving Speed - **Problem:** Troy's family traveled 360 miles. They drove 120 miles in the first 2 hours and then stopped for an hour to eat. If the entire trip, including the stop, took seven hours, what was their average driving speed? - **Concepts Involved:** Average speed calculation, distance and time relationships. #### Identifying Function Types - **Task:** Match the given problems to their corresponding function types. 1. **Linear** 2. **Quadratic** 3. **Rational** 4. **Radical** 5. **Exponential** Both the problems and the function types provided align closely with key mathematical concepts often discussed in middle and high school mathematics courses. Understanding these foundational problems and their solutions helps in grasping more complex mathematical principles.
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