If α and β are the zeros of the quadratic polynomial such that α + β = 24 and α - β = 8, find a quadratic polynomial having α and β as its zeros.
Understand the Problem
The question set involves solving various algebraic and graphical representation problems related to quadratic polynomials, distance and age problems, and equations of linear systems. Each problem asks the user to either find a specific value, form equations, or represent situations algebraically and graphically.
Answer
The number of rides on the Giant Wheel is 4, and the number of times she played Hoopla is 2.
Answer for screen readers
The number of rides on the Giant Wheel is 4, and the number of times she played Hoopla is 2.
Steps to Solve
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Identifying the Variables Let ( x ) represent the number of rides on the Giant Wheel. According to the problem, the number of times she played Hoopla is half the number of rides, so we can express this as ( \frac{x}{2} ).
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Setting Up the Equation for Costs Each ride costs Rs. 3, and each Hoopla game costs Rs. 4. Thus, the total cost from the rides is ( 3x ) and from games is ( 4 \left(\frac{x}{2}\right) = 2x ).
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Formulating the Total Cost Equation The total amount spent is given as Rs. 20, leading us to the equation: $$ 3x + 2x = 20 $$
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Simplifying the Equation Combine like terms: $$ 5x = 20 $$
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Solving for ( x ) Divide both sides by 5: $$ x = 4 $$
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Finding the Number of Hoopla Games Since the number of times she played Hoopla is: $$ \frac{x}{2} = \frac{4}{2} = 2 $$
The number of rides on the Giant Wheel is 4, and the number of times she played Hoopla is 2.
More Information
Akhila spent a total of Rs. 20, which was distributed among the Giant Wheel rides and the Hoopla games. She had four rides and played Hoopla two times.
Tips
- Forgetting to divide the number of rides by 2 when calculating Hoopla games.
- Not correctly setting up the total cost equation, which may lead to wrong conclusions.
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