The product of 9 and the sum of three times a number and 8 is 180. W...
The product of 9 and the sum of three times a number and 8 is 180. What is the number?
Solving the Algebraic Equation
The problem states: "The product of 9 and the sum of three times a number and 8 is 180." We can translate this directly into an algebraic equation and then solve for the unknown number.
Step-by-Step Solution
Let 'x' represent the unknown number. The sum of three times a number and 8: 3x + 8 The product of 9 and the sum: 9 * (3x + 8) The problem states this product equals 180: 9 * (3x + 8) = 180 Now we solve for x: 1. Distribute the 9: 27x + 72 = 180 2. Subtract 72 from both sides: 27x = 108 3. Divide both sides by 27: x = 4 Therefore, the number is 4.
Checking the Solution
We can verify our answer by plugging x = 4 back into the original equation:
9 * (3 * 4 + 8) = 180 9 * (12 + 8) = 180 9 * 20 = 180 180 = 180
The equation holds true, confirming our solution.
Real-World Applications
While this specific problem might seem abstract, the underlying skills of translating word problems into algebraic equations and solving for unknowns are crucial in various fields. These include finance (calculating interest or loan payments), engineering (determining material quantities or forces), and even everyday tasks like adjusting recipes or calculating distances for travel.
Relating to Current Trends
Problem-solving skills, particularly in STEM fields, are increasingly important in today's rapidly evolving technological landscape. The ability to break down complex problems, translate them into mathematical models, and find solutions is highly sought after in many industries.
Frequently Asked Questions (FAQ)
How do I translate word problems into algebraic equations?
Look for keywords like "sum," "difference," "product," "quotient," and "times." These indicate the mathematical operations (+, -, *, /) to use. Represent the unknown quantity with a variable (like 'x') and build the equation based on the relationships described in the problem.
What are some common mistakes to avoid when solving algebraic equations?
Be careful with the order of operations (PEMDAS/BODMAS). Also, remember to perform the same operation on both sides of the equation to maintain balance.
Call to Action
Ready to tackle more algebra challenges? Try searching for similar word problems online or explore interactive math platforms to practice your skills. Understanding algebra is a fundamental building block for many advanced concepts, so keep learning and practicing!
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