Understanding the Car Sales Data Table

The question asks us to analyze a table showing the number of cars sold by five different dealers (A, B, C, D, E) over six months in 2018. We need to calculate a specific ratio based on these sales figures.

Here is the data provided in the table:

Calculating Total Sales for Dealer B in Specific Months

First, we need to find the total number of cars sold by dealer B in January, April, and June. We locate the rows for these months and the column for Dealer B.

• Sales by Dealer B in January: 600
• Sales by Dealer B in April: 580
• Sales by Dealer B in June: 620

The total sales for Dealer B in these three months is the sum of these values:

\text{Total B (Jan, Apr, Jun)} = 600 + 580 + 620

\text{Total B (Jan, Apr, Jun)} = 1800

Calculating Total Sales for Dealers A and D in March

Next, we need to find the total number of cars sold by dealers A and D specifically in March. We locate the row for March and the columns for Dealer A and Dealer D.

• Sales by Dealer A in March: 628
• Sales by Dealer D in March: 722

The total sales for Dealers A and D in March is the sum of these values:

\text{Total (A + D) in March} = 628 + 722

\text{Total (A + D) in March} = 1350

Determining the Required Ratio

The question asks for the ratio of the total number of cars sold by dealer B in January, April and June to the total number of cars sold by dealers A and D in March.

This ratio is:

\text{Ratio} = \frac{\text{Total B (Jan, Apr, Jun)}}{\text{Total (A + D) in March}} = \frac{1800}{1350}

Simplifying the Ratio

To simplify the ratio \(\frac{1800}{1350}\), we can divide both the numerator and the denominator by their greatest common divisor (GCD). We can start by dividing by common factors.

• Divide both by 10: \(\frac{1800 \div 10}{1350 \div 10} = \frac{180}{135}\)
• Both 180 and 135 are divisible by 5 (since they end in 0 and 5): \(\frac{180 \div 5}{135 \div 5} = \frac{36}{27}\)
• Both 36 and 27 are divisible by 9: \(\frac{36 \div 9}{27 \div 9} = \frac{4}{3}\)

The simplified ratio is \(4 : 3\).

Conclusion

Based on the calculations, the ratio of the total number of cars sold by dealer B in January, April and June to the total number of cars sold by dealers A and D in March is \(4 : 3\).

Revision Table: Key Calculations

Additional Information: Ratio Concepts

A ratio is a comparison of two numbers or quantities. It shows how many times one value is contained within the other. Ratios can be written in several ways:

• Using a colon (e.g., \(a : b\))
• As a fraction (e.g., \(\frac{a}{b}\))
• Using the word "to" (e.g., \(a \text{ to } b\))

When working with ratios, it's standard practice to simplify them to their lowest terms, just like simplifying fractions. This involves dividing both parts of the ratio by their greatest common divisor. Ratios are commonly used in data analysis to compare different categories or time periods, as seen in this car sales data problem.