Question

Which expression can represent 70% of x?
3 (StartFraction x Over 4 EndFraction) minus one-half (StartFraction x Over 10 EndFraction)
3 (StartFraction x Over 4 EndFraction) minus (StartFraction x Over 10 EndFraction)
(StartFraction x Over 2 EndFraction) + (StartFraction x Over 10 EndFraction)
(StartFraction x Over 2 EndFraction) + one-half (StartFraction x Over 4 EndFraction)

Answer 1

To represent 70% of \( x \), we can express it as:

\[
0.7x \quad \text{or} \quad \frac{7}{10}x
\]

Now let's analyze the given expressions one by one to determine which one equals \( 0.7x \) or \( \frac{7}{10}x \).

1. **\( 3 \left( \frac{x}{4} \right) - \frac{1}{2} \left( \frac{x}{10} \right) \)**:
\[
= \frac{3x}{4} - \frac{1}{2} \cdot \frac{x}{10}
\]
\[
= \frac{3x}{4} - \frac{x}{20}
\]
To subtract these fractions, convert them to have a common denominator (which is 20):
\[
= \frac{3 \cdot 5x}{20} - \frac{x}{20} = \frac{15x}{20} - \frac{x}{20} = \frac{14x}{20} = \frac{7x}{10}
\]

2. **\( 3 \left( \frac{x}{4} \right) - \left( \frac{x}{10} \right) \)**:
\[
= \frac{3x}{4} - \frac{x}{10}
\]
Convert to a common denominator (which is 20):
\[
= \frac{3 \cdot 5x}{20} - \frac{2x}{20} = \frac{15x}{20} - \frac{2x}{20} = \frac{13x}{20}
\]

3. **\( \left( \frac{x}{2} \right) + \left( \frac{x}{10} \right) \)**:
\[
= \frac{5x}{10} + \frac{x}{10} = \frac{6x}{10} = \frac{3x}{5}
\]

4. **\( \left( \frac{x}{2} \right) + \frac{1}{2} \left( \frac{x}{4} \right) \)**:
\[
= \frac{x}{2} + \frac{1}{2} \cdot \frac{x}{4} = \frac{x}{2} + \frac{x}{8}
\]
Convert to a common denominator (which is 8):
\[
= \frac{4x}{8} + \frac{x}{8} = \frac{5x}{8}
\]

After calculating all expressions, we find that the first expression, \( 3 \left( \frac{x}{4} \right) - \frac{1}{2} \left( \frac{x}{10} \right) \), simplifies to \( \frac{7x}{10} \), which is equal to \( 0.7x \).

Thus, the correct answer is:

**\( 3 \left( \frac{x}{4} \right) - \frac{1}{2} \left( \frac{x}{10} \right) \)**.