Find a number such that ¼ of the number is 50 less than 2/3 of the number.

To find a number such that \( \frac{1}{4} \) of the number is 50 less than \( \frac{2}{3} \) of the number, let's represent the number by \( x \).

The problem can be translated into the equation:

\[
\frac{1}{4}x = \frac{2}{3}x - 50
\]

Now, let's solve this equation step by step.

1. **Eliminate the fractions**: Multiply every term by 12 (the least common multiple of 4 and 3) to eliminate the fractions.

\[
12 \times \frac{1}{4}x = 12 \times \left(\frac{2}{3}x - 50\right)
\]

This simplifies to:

\[
3x = 8x - 600
\]

2. **Isolate \( x \)**: Subtract \( 8x \) from both sides.

\[
3x - 8x = -600
\]

This simplifies to:

\[
-5x = -600
\]

3. **Solve for \( x \)**: Divide both sides by \(-5\).

\[
x = \frac{-600}{-5} = 120
\]

Thus, the number is \( \boxed{120} \).

Would you like more details on this solution, or do you have any questions?

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Here are 5 related questions for further practice:

1. Find a number such that \( \frac{1}{3} \) of the number is 40 less than \( \frac{5}{6} \) of the number.
2. Find a number such that \( \frac{1}{5} \) of the number is 30 more than \( \frac{1}{2} \) of the number.
3. If \( \frac{2}{5} \) of a number is equal to 60, what is the number?
4. Solve for a number where \( \frac{3}{4} \) of it is equal to \( \frac{2}{3} \) of 90.
5. Find a number such that \( \frac{1}{6} \) of the number is 20 less than \( \frac{3}{4} \) of the number.

**Tip:** When solving equations with fractions, multiplying through by the least common multiple of the denominators can simplify the process.

Learn how to solve equations involving fractions with a detailed step-by-step solution. Practice problems included. Suitable for students in Grades 7-9.

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