The distance D that the spring in a produce scale

Question

The distance D that the spring in a produce scale stretches is directly proportional to the weigh W of the fruits and vegetables placed in the pan. If 5 pounds of apples stretch the spring 0.3 inches, how far will 7 pounds of oranges stretch the spring?

 

 

Write an equation and solve.

Answer 1

For the formula, you know the relationship for distance stretched and weight is directly proportional...That is distance stretched is a constant multiple of the weight of the fruit, so D=k*W where k is some undetermined constant of proportionality.  The next part you are given information to solve for k. Rearranging the formula you get k =D/W. They tell you that for W=5lbs, D=0.3in. Therefore k=0.3in/5lbs=0.006in/lbs.  now the complete formula with the new k is D=0.06W.  So for your new W=7lbs, you know D=0.06in/lbs*7lbs=0.42in.  This should make sense since slightly more weight should stretch the spring slightly more. 

 

Hope this helps!