Final answer:
To find y when x=40 lbs, we first determine the constant of variation (k) using the given information that y=120 lbs when x=50 lbs, which results in k=2.4. Using the direct variation formula y=kx, we substitute k=2.4 and x=40 lbs to find that y=96 lbs.
Step-by-step explanation:
You've stated that y varies directly with x and provided the equation y=120 lbs when x=50 lb. To find y when x=40 lbs, we can use the concept of direct variation to set up a ratio since y is directly proportional to x. The equation for direct variation is y=kx, where k is the constant of variation.
We first find the constant of variation using the given values: y=120 when x=50, so k=y/x
=120/50
=2.4.
Now, to find y when x=40 lbs, we plug x=40 and k=2.4 into the direct variation formula:
y = kx
= 2.4(40)
= 96 lbs.
Therefore, if x=40 lbs, then y=96 lbs.