Question

name _______________________________ dat

1. the value of y varies directly with x. if x = 40 when y = 36, find the value of x when y = 45.

Explanation:

Step1: Define direct variation

Direct variation means $y = kx$, where $k$ is the constant of variation.

Step2: Solve for constant $k$

Substitute $x=40$, $y=36$:
$$k = \frac{y}{x} = \frac{36}{40} = \frac{9}{10}$$

Step3: Find $x$ when $y=45$

Rearrange $y = kx$ to $x = \frac{y}{k}$, substitute $y=45$, $k=\frac{9}{10}$:
$$x = \frac{45}{\frac{9}{10}} = 45 \times \frac{10}{9} = 50$$

Answer:

50