Question

If varies directly with y and x = 6 m when y = 15, find x when y = 20

Answer 1

If x varies directly with y, then :

●  Increase in x results in increase of y

●  Decrease in x results in decrease of y

●  It is represented by : x ∝ y

$\mathsf{\bigstar\;\;If\;x\;varies\;directly\;with\;y\;then : \large\boxed{\mathsf{\dfrac{x_1}{x_2} = \dfrac{y_1}{y_2}}}}$

Here : x₁ = 6 and y₁ = 15 and x₂ = x₂ and y₂ = 20

Substituting the values we get :

$\mathsf{\implies \dfrac{6}{x_2} = \dfrac{15}{20}}$

$\mathsf{\implies x_2 = \dfrac{20 \times 6}{15}}$

$\mathsf{\implies x_2 = 8}$

Answer : x = 8 when y = 20

Answer 2

Answer:

x = 8

Step-by-step explanation:

Given that x varies directly as y then the equation relating them is

x = ky ← k is the constant of variation

To find k use the condition x = 6 when y = 15

k = $\frac{x}{y}$ = $\frac{6}{15}$ = 0.4

x = 0.4y ← equation of variation

When y = 20, then

x = 0.4 × 20 = 8