225% of a number is 145. Find the 150% of that number.

Options

A. 96
B. `99.66`
C. `96.66`
D. `966`

Answer

To solve the problem step by step, we need to find the number based on the information given and then calculate 150% of that number.

### Step 1: Understand the given information
We know that 225% of a number is equal to 145. Let's denote the unknown number as \( x \).

### Step 2: Set up the equation
From the information provided, we can write the equation:
\[ 225\% \text{ of } x = 145 \]
This can be expressed mathematically as:
\[ \frac{225}{100} \times x = 145 \]

### Step 3: Simplify the equation
To eliminate the fraction, we can multiply both sides of the equation by 100:
\[ 225x = 14500 \]

### Step 4: Solve for \( x \)
Now, divide both sides by 225 to find \( x \):
\[ x = \frac{14500}{225} \]

### Step 5: Calculate \( x \)
Now we can simplify \( \frac{14500}{225} \):
1. First, we can simplify the fraction:
- Divide both the numerator and the denominator by 25:
\[ x = \frac{580}{9} \]

### Step 6: Find 150% of \( x \)
Now that we have \( x \), we need to find 150% of \( x \):
\[ 150\% \text{ of } x = \frac{150}{100} \times x = 1.5 \times x \]
Substituting the value of \( x \):
\[ 1.5 \times \frac{580}{9} = \frac{870}{9} \]

### Step 7: Calculate \( \frac{870}{9} \)
Now we divide:
\[ \frac{870}{9} \approx 96.67 \]

### Conclusion
Thus, 150% of the number is approximately \( 96.67 \).

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