Solve for a Different Variable with Directly and Indirectly

Direct and Indirect Variation - How it Works - Video

Terminology for Variation - Directly and Inversely

Guidelines for Solving Variation Problems

Guidelines for Solving Variation Problems:

1 - Write a general formula that involves the variables and a constant (proportion) or b or any letter

2 - Find the value of b in guideline 1 by substituting the initial data given in the statement

3 - Substitute the value of b in guideline 2 into the formula of guideline 1, obtaining a specific formula that involves the variables

4 - Use the new data to solve the problem

Example 1

Example 1:

When writing down formulas with different variables, I would write down all the different variables or highlight so you know what are you dealing with. Remember there will always be one more because because of the constant. 

W is our result. Directly means that we multiply the variables and indirectly means we divide the variables. 

Our first step is write down our formula. We know the result is w and our constant is b. We also know that anything that varies directly goes in the numerator and anything that varies indirectly goes in the denominator. Let's set up our formula.

w = b * (v/n2) - Guideline 1

Now we need to find b, our constant. So let's substitute the numbers for each variable and solve for b - Guideline 2.

Now we know what b, our constant is. It is 5. So we can write our formula with a number instead of a letter, w = 5 * (v/n2) - Guideline 3, which means that we can find any w, when given v and n - Guideline 4.

Now you might see the constant intermingled with the other variables. We have them separate so you can see what is happen better.

Example 2

Example 2:

When writing down formulas with different variables, I would write down all the different variables or highlight so you know what are you dealing with. Remember there will always be one more because because of the constant. 

W is our result. Directly means that we multiply the variables and indirectly means we divide the variables. 

Our first step is write down our formula. We know the result is w and our constant is b. We also know that anything that varies directly goes in the numerator and anything that varies indirectly goes in the denominator. Let's set up our formula.

w = b * (2x + t) / sqrt(h) - Guideline 1

This one is a bit different because we have the word sum. The same applies to difference of, product of, and quotient of. We have to treat each one has one entity in parenthesis. So the sum of 2x and t is (2x + t).

Now we need to find b, our constant. So let's substitute the numbers for each variable and solve for b - Guideline 2.

Now we know what b, our constant is. It is -5/4. So we can write our formula with a number instead of a letter, w =  (-5/4) * (2x + t) / sqrt(h) - Guideline 3, which means that we can find any w, when given v and n - Guideline 4. 

Now you might see the constant intermingled with the other variables. We have them separate so you can see what is happen better.

Example 3

Example 3:

When writing down formulas with different variables, I would write down all the different variables or highlight so you know what are you dealing with. Remember there will always be one more because because of the constant. 

W is our result. Directly means that we multiply the variables and indirectly means we divide the variables. 

Our first step is write down our formula. We know the result is r and our constant is b. We also know that anything that varies directly goes in the numerator and anything that varies indirectly goes in the denominator. Let's set up our formula.

r = b * v2 - Guideline 1

Now we need to find b, our constant. So let's substitute the numbers for each variable and solve for b - Guideline 2.

Now we know what b, our constant is. It is 1/30. So we can write our formula with a number instead of a letter, w =  (1/30) * v2 - Guideline 3, which means that we can find any w, when given v - Guideline 4. 

Now you might see the constant intermingled with the other variables. We have them separate so you can see what is happen better.

Since we want to know how the range of how it will go horizontally when going 80 mi/hr. We have our formula, w =  (1/30) * v2. So let's substitute.

Now we know the horizontal distance the car will go if going 80 mi/hr off a ramp.

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