word problem, im stumped

[higby]

The distance d when a spring is stretched by a hanging object varies directly as the weight w of the object if the distance is 50 cm when the weight is 4 kg what is the distance when the weight is 5 kg?

 

[Mrspi]

The distance d when a spring is stretched by a hanging object varies directly as the weight w of the object if the distance is 50 cm when the weight is 4 kg what is the distance when the weight is 5 kg?

The "general form" when

y varies DIRECTLY as x is

y = k*x

"k" is known as the constant of variation.

Ok...you are told that d varies directly as w, so following the general pattern, we have

d = k*w

You're also told that the distance "d" is 50 cm when the weight "w" is 4 kg. Substitute 50 cm for d, and 4 kg for k:

50 cm = k* 4 kg

Solve that for k. Divide both sides by 4 kg:

(50 cm)/(4 kg) = k
You can reduce the fraction on the left side:
(25/2)(cm/kg) = k

And you can now write the specific formula for THIS direct variation:

d = (25/2)(cm/kg)*w

And you should be able to finish the problem. You want to find the distance "d" when the weight is 5 kg. Substitute 5 kg for w....