Question
N Eighty, decreased by three times a number, is the same as five times the number, increased by eight. Find the number.
Ask by Bird Evans. in the United States
Feb 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The number is 9.
Solution
Let's denote the number as \( x \).
Given:
- Eighty decreased by three times a number is the same as five times the number increased by eight.
We can set up the equation based on the given information:
\[ 80 - 3x = 5x + 8 \]
Now, we can solve this equation to find the value of \( x \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(80-3x=5x+8\)
- step1: Move the expression to the left side:
\(-3x-5x=8-80\)
- step2: Add and subtract:
\(-8x=8-80\)
- step3: Add and subtract:
\(-8x=-72\)
- step4: Change the signs:
\(8x=72\)
- step5: Divide both sides:
\(\frac{8x}{8}=\frac{72}{8}\)
- step6: Divide the numbers:
\(x=9\)
The solution to the equation is \( x = 9 \).
Therefore, the number is 9.
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Simplify this solution Extra Insights
To solve the equation, we first set up the expression from the problem: N Eighty - 3x = 5x + 8, where x is the unknown number. Rearranging gives us: N Eighty - 8 = 8x. Now, N Eighty is 80, leading to: 80 - 8 = 8x, so 72 = 8x. Dividing both sides by 8, we find x = 9. Celebrate! The unknown number is 9! 🎉 Now, if you were ever in doubt about your math skills, don’t fret! Math is all about practice, and finding the right approach can make all the difference. Try breaking down complex problems into smaller parts, writing out each step, and don't hesitate to double-check your work. Common mistakes often stem from simple blunders, so stay focused!
