When two parameters are linked in such a manner that a rise in one generates a commensurate reduction in the other and vice versa, is known as an inverse variation or indirect variation. This post will demonstrate how to define the unitary approach in inverse variation with solved examples. Step by Step Process used in the Unitary Method Inverse Variation Problems used makes it easy for you to understand the concept of 7th Grade Math Inverse Variations Using Unitary Method.
Unitary Method Inverse Variation
The unitary technique is concerned with assigning value to a single unit. The unitary technique may be used to compute costs, measures such as liters, and time. As a result, if a rise in one number causes a commensurate reduction in another, the quantities are said to be in inverse variation.
When one number decreases, another quantity increases proportionally, and the quantities are said to be in inverse variation. The change in both amounts must be the same.
Increase ——-> Decrease
or
Decrease ——-> Increase
How do you Do Inverse Variation in Unitary Method?
We know that the two variables can be correlated in such a way that if one rises, the other falls. When one falls, the other rises. Here are simple steps on how to solve inverse variation using the unitary method. Keep these below points in mind.
- When there are more guys on the job, it takes less time to do the work.
- More speed equals or takes less time to travel the actual same distance.
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Unitary Method Inverse Variation Questions
Let’s see the examples of Inverse Variation in Unitary Method.
Example 1:
16 typists working 4 hours a day for 18 days to type a book How many days will 6 typists labor for 8 hours to type the same book?
Solution:
16 typists working 4 hours each day to type a book in 18 days.
1 typist working 4 hours per day types a book in 18 * 16 days.
1 typist spent 1 hour each day typing a book in 18*16*4 days.
6 typists working for 1 hour each type a book (18*16*4)/6
6 typists working 8 hours each day type a book in (18*16*4)/(6*8) days.
As a result, 6 typists working 8 hours each day type a book in 24 days.
Example 2:
If 42 men can accomplish a task in 25 days, how long will it take 18 men to do the same task?
Solution:
This is an inverse variation scenario, which we will now address using the unitary technique.
The task may be completed in 25 days by 42 guys.
In (25 × 42) days, one guy may complete the task.
The task may be completed in days by 18 guys. (25 × 42)/18 days
As a result, 18 workers can do the job in 58 days.
Example 3:
There is enough food at a camp for 400 soldiers to eat for 30 days. How long will the food survive if 200 additional troops join the camp?
Solution:
This is an inverse variation scenario, which we will now address using the unitary technique.
Food lasts 30 days for 400 troops.
Food lasts (30 × 400) days for one soldier.
Since then, 200 more have joined. As a result, the total number of soldiers is now (400 + 200)=600..
Food lasts (30 × 400)/600 days for 600 troops.
As a result, food lasts for Approximately 20 days for 600 troops.
Example 4:
In 70 days, 25 employees can accomplish a task. In 35 days, how many employees will accomplish the same task?
Solution:
This is an inverse variation scenario, which we will now address using the unitary technique.
Workers required to finish the task in 70 days = 25
The worker required to accomplish the task in one day = (25 × 70)
Workers necessary to perform the task in 48 days = (25 × 70)/35
As a result, 50 employees are required to finish the task in 35 days.
FAQs on Inverse Variation using Unitary Method
1. What sorts of unitary methods are there?
The unitary approach may be classified into two types: direct variation and inverse variation.
2. What is the unitary percentage method?
The unitary approach can be used to calculate 100% of a quantity. For instance, if 15% of the number of marbles in a pot is 25, then 100% of the marbles will be 25 x 15 = 375
3. What exactly is a unitary method?
The unitary method is a method for determining the value of a single unit and then calculating the value of the requisite number of units using that value.