Analyzing Motorcycle Production Data for Ratio Calculation

The question asks us to find the ratio of the total production of motorcycles of type B in the years 2016 and 2018 to the total production of motorcycles of type D in the years 2013, 2015, and 2016, based on the provided table showing motorcycle production over six years.

Calculating Total Production for Type B Motorcycles

First, let's find the total production of type B motorcycles in the specified years, which are 2016 and 2018. We look at the row for Type B and find the values under the 2016 and 2018 columns.

• Production of Type B in 2016 = 88 thousand
• Production of Type B in 2018 = 92 thousand

Total production of Type B motorcycles in 2016 and 2018 is the sum of these values:

Total Type B production = 88 + 92 = 180 thousand

Using LaTeX for the calculation:

\( \text{Total Type B (2016, 2018)} = 88 + 92 = 180 \)

Calculating Total Production for Type D Motorcycles

Next, let's find the total production of type D motorcycles in the specified years, which are 2013, 2015, and 2016. We look at the row for Type D and find the values under the 2013, 2015, and 2016 columns.

• Production of Type D in 2013 = 103 thousand
• Production of Type D in 2015 = 102 thousand
• Production of Type D in 2016 = 95 thousand

Total production of Type D motorcycles in 2013, 2015, and 2016 is the sum of these values:

Total Type D production = 103 + 102 + 95 = 300 thousand

Using LaTeX for the calculation:

\( \text{Total Type D (2013, 2015, 2016)} = 103 + 102 + 95 = 300 \)

Determining the Ratio of Motorcycle Production

The question asks for the ratio of the total number of motorcycles of type B produced in 2016 and 2018 to the total number of motorcycles of types D produced in 2013, 2015 and 2016.

Ratio = (Total Type B production in 2016 and 2018) : (Total Type D production in 2013, 2015, and 2016)

Ratio = 180 : 300

To simplify the ratio, we can divide both numbers by their greatest common divisor. Both 180 and 300 are divisible by 60.

\( \frac{180}{60} = 3 \)

\( \frac{300}{60} = 5 \)

So, the simplified ratio is 3 : 5.

Using LaTeX for the ratio simplification:

\( \text{Ratio} = \frac{180}{300} = \frac{18}{30} = \frac{3}{5} \)

Thus, the ratio is 3:5.

Revision Table: Key Calculations

Additional Information on Ratios and Data Interpretation

Understanding ratios is crucial when analyzing data from tables. A ratio compares two quantities. In this problem, we compared the total production of one type of motorcycle over specific years to the total production of another type over different years. Simplifying the ratio helps in understanding the proportional relationship between the quantities.

• Ratio: A ratio is a way to compare two or more numbers. It shows how many times one number contains another. Ratios can be written as a:b, a/b, or "a to b".
• Simplifying Ratios: To simplify a ratio, divide all parts of the ratio by their greatest common divisor (GCD). This gives the ratio in its simplest form.
• Data Tables: Tables organize data into rows and columns, making it easier to read and extract specific information needed for calculations and comparisons like ratios. Each cell in the table contains a specific data point corresponding to the intersection of a row (e.g., motorcycle type) and a column (e.g., year).

This problem demonstrates how to extract specific data points from a table, perform calculations based on those points, and then express the result as a simplified ratio, a common task in data interpretation questions.