`(1)/(2)` is subtracted from a number and the difference is multiplied by 4. If 25 is added to the product and the sum is divided by 3, the result is equal to 10. Find the number

Options

A. `(3)/(5)`
B. `(7)/(4)`
C. `(6)/(7)`
D. `(2)/(3)`

Answer

Let's solve the problem step by step.

### Step 1: Define the variable
Let the unknown number be represented by \( x \).

### Step 2: Set up the equation
According to the problem, we first subtract \( \frac{1}{2} \) from the number \( x \):
\[ x - \frac{1}{2} \]
Next, we multiply this difference by 4:
\[ 4 \left( x - \frac{1}{2} \right) \]
Then, we add 25 to this product:
\[ 4 \left( x - \frac{1}{2} \right) + 25 \]
Finally, we divide the entire expression by 3, and this is equal to 10:
\[ \frac{4 \left( x - \frac{1}{2} \right) + 25}{3} = 10 \]

### Step 3: Eliminate the fraction
To eliminate the fraction, we multiply both sides of the equation by 3:
\[ 4 \left( x - \frac{1}{2} \right) + 25 = 30 \]

### Step 4: Simplify the equation
Now, we subtract 25 from both sides:
\[ 4 \left( x - \frac{1}{2} \right) = 30 - 25 \]
This simplifies to:
\[ 4 \left( x - \frac{1}{2} \right) = 5 \]

### Step 5: Divide by 4
Next, we divide both sides by 4:
\[ x - \frac{1}{2} = \frac{5}{4} \]

### Step 6: Solve for \( x \)
Now, we add \( \frac{1}{2} \) to both sides. First, we convert \( \frac{1}{2} \) to a fraction with a denominator of 4:
\[ \frac{1}{2} = \frac{2}{4} \]
So, we have:
\[ x = \frac{5}{4} + \frac{2}{4} \]
This simplifies to:
\[ x = \frac{7}{4} \]

### Final Answer
The number is \( \frac{7}{4} \).

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