If the number of cars sold of model D is 40500, what is the ratio between the number of cars sold of model D and E?

Options

A. `9:5`
B. `6:5`
C. `11:9`
D. `9:7`

Answer

To find the ratio between the number of cars sold of model D and model E, we can follow these steps:

### Step 1: Understand the given information
We know that the number of cars sold of model D is 40,500. We also have the degrees of the pie chart representing the cars sold for different models. Model D corresponds to 90 degrees.

### Step 2: Find the total degrees in a pie chart
A pie chart represents a whole circle, which is 360 degrees.

### Step 3: Calculate the number of cars sold for model E
From the information provided, model E corresponds to 75 degrees in the pie chart.

### Step 4: Find the value of 1 degree
To find the number of cars represented by 1 degree, we can use the number of cars sold for model D (40,500) and the degrees it represents (90 degrees).

\[ \text{Value of 1 degree} = \frac{\text{Number of cars sold of model D}}{\text{Degrees for model D}} = \frac{40500}{90} = 450 \]

### Step 5: Calculate the number of cars sold for model E
Now that we know the value of 1 degree is 450 cars, we can calculate the number of cars sold for model E:

\[ \text{Number of cars sold of model E} = \text{Value of 1 degree} \times \text{Degrees for model E} = 450 \times 75 = 33750 \]

### Step 6: Find the ratio of cars sold of model D to model E
Now we can find the ratio of the number of cars sold of model D to model E:

\[ \text{Ratio} = \frac{\text{Number of cars sold of model D}}{\text{Number of cars sold of model E}} = \frac{40500}{33750} \]

### Step 7: Simplify the ratio
To simplify the ratio, we can divide both numbers by their greatest common divisor (GCD).

Calculating the GCD of 40500 and 33750 gives us 6750. Now we can simplify:

\[ \frac{40500 \div 6750}{33750 \div 6750} = \frac{6}{5} \]

Thus, the ratio of the number of cars sold of model D to model E is:

\[ \text{Ratio} = 6:5 \]

### Final Answer
The ratio between the number of cars sold of model D and E is **6:5**.

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