A is 60% more than B and C is 45% less than twice the sum of B and A. By what percentage is C more than A?

Options

A. 75.25
B. 76.5
C. 78.75
D. 77.25

Answer

To solve the problem step by step, we will define the relationships between A, B, and C based on the information provided.

### Step 1: Define the relationship between A and B
Given that A is 60% more than B, we can express A in terms of B:
\[ A = B + 0.6B = 1.6B \]

**Hint:** Remember that "60% more" means you take the original amount (B) and add 60% of it to itself.

### Step 2: Calculate the sum of A and B
Now, we need to find the sum of A and B:
\[ A + B = 1.6B + B = 2.6B \]

**Hint:** When adding A and B, ensure you combine the coefficients correctly.

### Step 3: Define C in terms of B
Next, we know that C is 45% less than twice the sum of B and A:
\[ C = 2(A + B) - 0.45 \times 2(A + B) \]
Substituting the sum we found in Step 2:
\[ C = 2(2.6B) - 0.45 \times 2(2.6B) \]
\[ C = 5.2B - 0.9 \times 5.2B \]
\[ C = 5.2B - 4.68B = 0.52B \]

**Hint:** When calculating "45% less," remember to subtract 45% of the total from the total itself.

### Step 4: Find the difference between C and A
Now, we need to find out by what percentage C is more than A:
First, we find the difference:
\[ C - A = 0.52B - 1.6B = -1.08B \]

**Hint:** The difference between two quantities can be found by subtracting one from the other.

### Step 5: Calculate the percentage increase of C over A
To find the percentage by which C is more than A, we use the formula:
\[ \text{Percentage Increase} = \left( \frac{C - A}{A} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Increase} = \left( \frac{-1.08B}{1.6B} \right) \times 100 \]
\[ = \left( \frac{-1.08}{1.6} \right) \times 100 \approx -67.5\% \]

**Hint:** When calculating the percentage, make sure to multiply by 100 to convert the decimal to a percentage.

### Step 6: Interpret the result
Since the result is negative, it indicates that C is not more than A, but rather less than A by approximately 67.5%.

**Final Answer:** C is approximately 67.5% less than A.