When the proportions of one quantity change, the proportions of the other must also change! For example, if you buy more apples, you will have to spend more money, which is an example of direct proportionality. Let’s look at a definition of direct variation using the method of proportion, its formula, and some examples to get a better understanding of this topic.
What is meant by Direct Variation using the Method of Proportion?
When two quantities are linked in such a manner that a rise in one leads to a comparable increase in the other, this is known as ease of direct variation. Furthermore, a drop in one quantity causes a decrease in the other. If two quantities x and y are in direct proportion, then they are said to be in direct proportion.
x = ky
Example: Assume you increase the number of books in your bag. What will happen to its weight? It will also rise. This is known as direct proportionality. The ratio of the two quantities and their respective values will always remain constant while their two variables, x, and y, rise and decrease.
How to use Proportions for Direct Variation to Solve for x?
Now we’ll look at how to use the proportion technique to solve direct variations. We know that the two variables can be connected in such a way that when one rises, the other rises as well.
- Create a proportional relation, where y = kx is the direct variation equation.
- Substitute the given values in the formula.
- Find the unknown by simplifying further and that’s it.
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Examples of Direct Variation using Unitary Method of Proportion
We know that the two variables can be connected in such a way that when one rises, the other rises as well. Some examples of direct variations:
- More articles equal more money spent on purchases.
- More men at work equal more work done.
- More speed will result in more distance traveled in a given amount of time.
- Higher money borrowed results in more interest to pay.
- More working hours equals more work.
Direct Variation Unitary Method of Proportion Examples
Example 1.
A 6-kilogram bag of rice costs $60. How much would 16 kg of sugar cost?
Solution:
This is a case of direct variation, we will solve it using the proportional technique.
More rice comes at a higher work
In this case, the two amounts fluctuate immediately (Quantity of rice and cost of rice)
| Weight of rice(kg) | 6 | 16 |
| Cost | 60 | X |
Because they differ directly
As a result, 6/60 = 16/x (cross multiply)
6x = 60×16
x = (60×16)/6 = 160
As a result, the cost of 16 kg rice is $ 160.
Example 2.
What do 32 books cost if 8 drawing books cost $154?
Solution:
This is a case of direct variation, and we will solve it using the proportional technique.
The greater the number of drawing books, the higher the expense.
In this case, the two amounts fluctuate directly (Number of drawing books and cost of drawing books)
| No of drawing books | 8 | 32 |
| Cost | 154 | X |
Because they differ directly
As a result, 8/154 = 32/x (cross multiply)
8x = 154*32
x = (154*32)/8= 616
As a result, the cost of 32 drawing books is $616.
Example 3.
A worker is paid $630 for 9 days of work. How many days need he to work in order to earn $840?
Solution:
This is a case of direct variation, and we will solve it using the proportional method.
More money, more working days
In this case, the two amounts fluctuate directly. (Amount and number of days worked)
| No of working days | 9 | X |
| Payout | 630 | 840 |
Since they differ in a direct manner
As a result, 9/630 = x/840
630x = 840*9
x = (840*9)/630
As a result, 840 were earned by workers in 12 days
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FAQs on Direct Variation using Proportion Method
1. Is it true that proportionate means the same thing as equal?
When something is proportional to something else, it signifies that the values fluctuate in relation to each other, not that the values are equal. However, the proportionality constant acts as a multiplier.
2. What is the difference between direct and inverse proportion?
As the name implies, direct proportion states that to work in one quantity increase the value of the other quantity, and a decrease in one number decreases the value of the other item. Inverse proportion demonstrates an inverse connection between two provided values. It indicates that increasing one quantity reduces the value of the other, and vice versa.
3. How should the Direct Proportion Formula be represented?
The following steps will help you understand the direct proportion formula, which describes the connection between two quantities:
- Determine the two variables in the given problem.
- Determine which variation is the direct variation.
- y ∞ kx is a direct proportion formula.