Question
15. Lee wrote a 2-digit number. She divided it by 9 , added 24 , and double the result. Her final answer was 64 . What number did Lee write?
Ask by Vega Schwartz. in the United States
Feb 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Lee wrote the number 72.
Solution
Let's denote the 2-digit number that Lee wrote as \( x \).
According to the given information:
1. Lee divided the number by 9: \( \frac{x}{9} \)
2. Added 24: \( \frac{x}{9} + 24 \)
3. Doubled the result: \( 2 \times (\frac{x}{9} + 24) \)
4. The final answer was 64: \( 2 \times (\frac{x}{9} + 24) = 64 \)
Now, we can solve the equation to find the value of \( x \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(2\left(\frac{x}{9}+24\right)=64\)
- step1: Multiply the terms:
\(\frac{2x}{9}+48=64\)
- step2: Move the constant to the right side:
\(\frac{2x}{9}=64-48\)
- step3: Subtract the numbers:
\(\frac{2x}{9}=16\)
- step4: Cross multiply:
\(2x=9\times 16\)
- step5: Simplify the equation:
\(2x=144\)
- step6: Divide both sides:
\(\frac{2x}{2}=\frac{144}{2}\)
- step7: Divide the numbers:
\(x=72\)
The solution to the equation is \( x = 72 \).
Therefore, Lee wrote the number 72.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To find the 2-digit number Lee wrote, let's denote that number as \( x \). According to the problem, she first divided it by 9, which gives us \( \frac{x}{9} \). Then, she added 24 to this result: \[ \frac{x}{9} + 24 \] Next, she doubled this entire expression: \[ 2 \left( \frac{x}{9} + 24 \right) \] We know the final answer to this operation is 64: \[ 2 \left( \frac{x}{9} + 24 \right) = 64 \] Now, let's simplify and solve for \( x \): 1. Divide both sides by 2: \[ \frac{x}{9} + 24 = 32 \] 2. Subtract 24 from both sides: \[ \frac{x}{9} = 8 \] 3. Multiply both sides by 9 to solve for \( x \): \[ x = 72 \] Thus, the 2-digit number that Lee wrote is 72.
