Question

Suppose a varies directly as b and a varied inversely as c. Find b when a=8 and c=-3, if b=16 when c=2 and a=4

Answer 1

Answer:

Step-by-step explanation:

Step 1: Write the correct equation. Combined variation problems are solved using a combination of direct variation (y = kx), inverse variation Inverse, and joint variation (y = kxz) equations. When dealing with word problems, you should consider using variables other than x, y, and z, you should use variables that are relevant to the problem being solved. Also read the problem carefully to determine if there are any other changes in the combined variation equation, such as squares, cubes, or square roots.

Step 2: Use the information given in the problem to find the value of k, called the constant of variation or the constant of proportionality.

Step 3: Rewrite the equation from step 1 substituting in the value of k found in step 2.

Step 4: Use the equation found in step 3 and the remaining information given in the problem to answer the question asked. When solving word problems, remember to include units in your final answer.

Example 1 – If y varies directly as x and inversely as z, and y = 24 when x = 48 and z = 4, find x when y = 44 and z = 6.

Step 1: Write the correct equation. Combined variation problems are solved using a combination of variation equations. In this case we will combine the direct and inverse variation equations.  

Step 1

Step 2: Use the information given in the problem to find the value of k. In this case, you need to find k when x = 48, y = 24, and z = 4.  

Step 2

Step 3: Rewrite the equation from step 1 substituting in the value of k found in step 2.  

Step 3

Step 4: Use the equation found in step 3 and the remaining information given in the problem to answer the question asked. In this case, you need to find x when y = 44 and z = 6.  

Step 4

Example 2 – If f varies directly as g and inversely as the square of h, and f = 20 when g = 50 and h = 5, find f when g = 18 and h = 6.