Math Problem Statement
Solution
The problem provided is:
"Eight times the difference of twice a number and 10 yields the number increased by 40. Find the number."
Let's break this down into an equation step by step:
- Let the unknown number be represented as .
- Twice the number is .
- The difference of twice the number and 10 is .
- Eight times this difference is .
- This is said to equal the number increased by 40, which is .
Now, we can set up the equation:
Solving the equation:
-
Distribute the 8 on the left side:
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Move to the left side by subtracting from both sides:
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Add 80 to both sides:
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Solve for by dividing both sides by 15:
Thus, the number is .
Would you like further details on this solution or have any questions? Here are some related questions you might consider:
- How do we check if the solution is correct?
- How does the concept of translating word problems into equations work?
- What if the problem had a different multiplier instead of 8?
- How would the equation change if it said "decreased by 40" instead of "increased by 40"?
- What are other examples of linear equations involving a single variable?
Tip: When solving word problems, always define the variable clearly and build the equation step-by-step based on the given conditions.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Formulas
8(2x - 10) = x + 40
Theorems
Linear Equation Solving
Suitable Grade Level
Grades 7-9