Understanding Bike and Truck Production Ratios

The question asks for the ratio of the combined production of trucks by company H and company I to the combined production of bikes by company J and company K, based on the data provided in the table.

First, let's look at the production data from the table:

Calculating Combined Truck Production

We need to find the total truck production by company H and company I.

• Truck production by company H = 400
• Truck production by company I = 300

Combined truck production by H and I = $400 + 300 = 700$

Calculating Combined Bike Production

Next, we find the total bike production by company J and company K.

• Bike production by company J = 350
• Bike production by company K = 400

Combined bike production by J and K = $350 + 400 = 750$

Determining the Required Ratio

The required ratio is (Truck production by H and I together) : (Bike production by J and K together).

Ratio = $700 : 750$

Simplifying the Ratio

To simplify the ratio $700 : 750$, we can divide both numbers by their greatest common divisor. Both 700 and 750 are divisible by 50.

• $700 \div 50 = 14$
• $750 \div 50 = 15$

So, the simplified ratio is $14 : 15$.

Using mathematical notation:

$$ \text{Ratio} = \frac{\text{Truck (H+I)}}{\text{Bike (J+K)}} = \frac{700}{750} $$

$$ \text{Ratio} = \frac{700 \div 50}{750 \div 50} = \frac{14}{15} $$

The ratio of the production of truck by company H and I together to the production bike by company J and K together is $14 : 15$.

Revision Table: Key Calculations

Additional Information on Ratios and Proportions

A ratio is a comparison of two quantities. It shows how much of one quantity there is compared to another quantity. Ratios can be written in several ways, such as $a:b$, $a/b$, or "a to b".

Simplifying a ratio involves dividing both parts of the ratio by the same number, usually their greatest common divisor (GCD), to express the ratio in its simplest form. This is similar to simplifying a fraction.

In this problem, we calculated a ratio based on combined values from a dataset. This is a common application of ratios in data analysis.