The table given below shows the production of bike and truck by five companies. Production Companies Bike Truck G 800 600 H 550 400 I 600 300 J 350 700 K 400 750 What is the ratio of the production of truck by company H and I together to the production bike by company J and K together?
14 : 15
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:
| Production | Companies | Bike | Truck |
|---|---|---|---|
| G | 800 | 600 | |
| H | 550 | 400 | |
| I | 600 | 300 | |
| J | 350 | 700 | |
| K | 400 | 750 |
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
| Category | Companies | Production | Calculation | Result |
|---|---|---|---|---|
| Truck | H & I | 400 (H), 300 (I) | $400 + 300$ | 700 |
| Bike | J & K | 350 (J), 400 (K) | $350 + 400$ | 750 |
| Ratio | (Truck H+I) : (Bike J+K) | 700, 750 | $700 \div 50 : 750 \div 50$ | 14 : 15 |
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.
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