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Solve Change Problem Quadratic Equation and Fractions Step by Step
Published on September 11, 2026
Algebra
Learn how to calculate shopping change, solve a quadratic equation using the quadratic formula, and evaluate fraction operations with clear step-by-step explanations.
Question
A student buys 3 notebooks for $4.50 each and 2 pens for $1.25 each. She pays with $20. Calculate the amount of change she receives. Then solve the following equation: 2x² + 5x − 12 = 0 Show your answer using the quadratic formula: x = \frac{-b ± \sqrt{b² − 4ac}}{2a} Finally, calculate: $$ \frac{3}{4} + \frac{5}{8} - \frac{1}{2} $$ Explain each step clearly, and keep the mathematical symbols, superscripts, fractions, parentheses, and line breaks exactly as provided.
Answer
Part 1: Change Calculation
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Calculate the total cost of the notebooks and pens:
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Subtract the total cost from the amount paid to find the change:
Part 2: Solving the Quadratic Equation
Given the equation
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Substitute the values into the quadratic formula:
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Simplify the terms inside the square root (the discriminant):
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Solve for the two possible values of
:
Part 3: Fraction Calculation
To solve
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Convert all fractions to have a denominator of
: -
Perform the addition and subtraction:
Final Answers:
Change:
Fraction result:
Change:
Fraction result: