Question

Given that y varies directly as x and y = 18 when x = 6

Find the value of y when x=5
find the value of x when y=30
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Answer 1

Answer:   y = 15,    x = 10

Step-by-step explanation:

NOTE: "varies directly" is of the form    $\dfrac{y}{x}=k$  where k is the constant of proportionality.

First, input the given x and y-values to find k

$\dfrac{y}{x}=k\qquad \qquad \text{Given: y=18, x=6}\\\\\dfrac{18}{6}=k\\\\\boxed{3=k}$

Next, input the given value and k = 3 to solve for the missing variable.

$x = 5\\\\\dfrac{y}{5}=3\\\\\large\boxed{y = 15}\\\\\\y=30\\\\\dfrac{30}{x}=3\\\\\dfrac{30}{3}=x\\\\\large\boxed{10 = x}$