Question 4.8.1: Solving Variation Problems OBJECTIVE Solve variation problem...
Solving Variation Problems
OBJECTIVE
Solve variation problems.
Step 1 Write the equation with the constant of variation, k.
Step 2 Substitute the given values of the variables into the equation in Step 1 to find the value of the constant k.
Step 3 Rewrite the equation in Step 1 with the value of k from Step 2.
Step 4 Use the equation from Step 3 to answer the question posed in the problem.
Suppose varies as x and x=\frac{4}{3} when y=20. Find y when x = 8.
\begin{aligned}y &=k x & & y \text { varies as } x . \\20 &=k\left(\frac{4}{3}\right) & & \text { Replace } y \text { with } 20 \text { and } x \text { with } \frac{4}{3} . \\20\left(\frac{3}{4}\right) &=k\left(\frac{4}{3}\right)\left(\frac{3}{4}\right) & & \text { Multiply both sides by } \frac{3}{4} . \\15 &=k & & \text { Simplify to solve for } k . \\y &=15 x & & \text { Replace } k \text { with } 15 . \\y &=15(8) & & \text { Replace } x \text { with } 8 . \\y &=120 & & \text { Simplify. }\end{aligned}
So when y = 120 when x = 8.