The sum of 55% of a number and 40 % of the same number is 180.5 . What is 80% of that number ?

Options

A. 134
B. 152
C. 148
D. 166

Explanation

To solve the problem step by step, let's break it down:

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

### Step 2: Set up the equation
According to the problem, the sum of 55% of the number and 40% of the same number is 180.5. We can express this mathematically as:
\[ 0.55x + 0.40x = 180.5 \]

### Step 3: Combine like terms
Now, combine the percentages:
\[ (0.55 + 0.40)x = 180.5 \]
\[ 0.95x = 180.5 \]

### Step 4: Solve for \( x \)
To find \( x \), divide both sides of the equation by 0.95:
\[ x = \frac{180.5}{0.95} \]

### Step 5: Calculate \( x \)
Now, perform the division:
\[ x = \frac{180.5 \times 100}{95} = \frac{18050}{95} \]
Calculating this gives:
\[ x = 190 \]

### Step 6: Find 80% of \( x \)
Now that we have \( x \), we need to find 80% of \( x \):
\[ 0.80x = 0.80 \times 190 \]

### Step 7: Calculate 80% of \( x \)
Calculating this gives:
\[ 0.80 \times 190 = \frac{80}{100} \times 190 = \frac{15200}{100} = 152 \]

### Final Answer
Thus, 80% of the number is:
\[ \boxed{152} \]

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