Questions and Answers
Quadratic equations are never used to solve word problems.
False
If x represents the width of the patio around a rectangular pool with dimensions of 40 ft by 60 ft, which of the following equations could be used to solve the problem where the patio area equals the area of the pool?
If one leg of a right triangle measures 96 inches and the length of the hypotenuse is twice the other leg, which of the following equations represents the Pythagorean Theorem in general form?
The product of two consecutive odd integers is 2,115. Which of the following quadratic equations could be used to solve for those integers?
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If the square of one number is 23 less than the square of a second number, and the second number is 1 more than the first number, what is the quadratic equation that represents this problem?
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What is the rate of Ben's boat if it will take 1½ hours longer to go 12 miles up a river than to return, with a current of 2 miles an hour?
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What was Loren's rate if he drove 200 miles at a certain rate, and his wife, Lois, drove 100 miles at a rate 10 mph slower, and they would have arrived 30 minutes sooner if Loren had driven for the entire trip?
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How long would Tammy take to do the job alone if they can wash cars, clean the pool, and mow the lawn in one hour and 20 minutes, with Jeri taking twice as long as Tammy?
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How long would Ron and Lee take to frame the cabin alone if Lee can frame it in 4 days less than Ron, and together they take 4 45 days?
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How many shares did Ed buy if he bought $2,000 in stock shares one week before the stock price dropped $10.00, and he could have bought 10 more shares for the same amount?
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What is Mark's age now if the square of his age 3 years ago is 6 times the age he will be in 9 years?
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Study Notes
Quadratic Equations in Word Problems
- Quadratic equations can be useful in solving various real-life scenarios, contrary to the myth that they cannot be applied to word problems.
Rectangular Pool and Patio Area
- For a patio surrounding a 40 ft by 60 ft pool, if the patio area equals the pool's area, set the equation: x² + 50x - 600 = 0, where x is the patio width.
Right Triangle Pythagorean Theorem
- In a right triangle with one leg measuring 96 inches and the hypotenuse being twice the other leg, the equation is 3x² - 9216 = 0 for finding the length of the other leg x.
Consecutive Odd Integers
- The product of two consecutive odd integers is 2,115. This leads to the quadratic equation: x² + 2x - 2,115 = 0.
Difference of Squares Problem
- If the square of one number is 23 less than the square of another number, represented by the equation x² + 23 = x² + 2x + 1 (where x is the smaller number), then solve to find both numbers.
Ben's Boat Problem
- Ben's boat travels 12 miles upstream, taking 1.5 hours longer due to a 2 mph current. His boat's speed is determined to be 6 mph.
Loren and Lois' Travel Rates
- Loren travels 200 miles while Lois goes 100 miles at a rate 10 mph slower. If Loren handled the entire trip, they would save 30 minutes. His rate is calculated to be 50 mph.
Task Completion by Three Girls
- Laura, Tammy, and Jeri can complete various household tasks in 1 hour and 20 minutes. Jeri would take twice as long as Tammy. Tammy's individual completion time is deduced to be 3 hours.
Framing a Cabin Problem
- Lee frames a cabin in 4 days less than Ron. Together, they can complete the cabin framing job in 4.75 days. Individual times found: Ron takes 12 days; Lee takes 8 days.
Stock Shares Purchase
- Ed bought $2,000 worth of stock a week before a price drop of $10. He could have purchased 10 more shares if he had waited, leading to the conclusion that he initially bought 40 shares.
Age Problem Involving Mark
- Three years ago, the square of Mark's age was 6 times his future age in nine years. This leads to the conclusion that his current age is 15.
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Description
Explore various real-life problems that can be solved using quadratic equations, from pool and patio areas to right triangle dimensions. This quiz includes challenges based on word problems involving consecutive integers and more. Test your skills and see how quadratic equations apply to everyday situations.
