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Y varies directly with x and y=120 lbs when x=50 lb find y if x=40 lbs

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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.

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