Assume that y varies inversely as x. If x = 12 when y = 9, what is x when y = -3?

Question

Genesis Allen · Accepted Answer

undefined To find x when y = -3, we can use the inverse variation formula: y = k/x.

First, we need to find the constant of variation, k. We can do this by substituting the given values into the formula: 9 = k/12.

Solving for k, we multiply both sides of the equation by 12: 9 * 12 = k. This gives us k = 108.

Now that we have the value of k, we can substitute it into the formula and solve for x when y = -3: -3 = 108/x.

To isolate x, we multiply both sides of the equation by x: -3x = 108.

Dividing both sides by -3, we find that x = -36.

Therefore, when y = -3, x is equal to -36.

Kennedy Adams · Answer

#x = -36#

The basic inverse variation equation is

#xy = k#

where #k# is the constant of variation. In order to write the equation that reflects this relationship, we must find #k#. We use the known relationship of #x = 12# and #y = 9# to find #k#. Substituting in the basic equation, we will find #k#:

#xy = k#

#(12)(9) = k#

#108 = k#

This then yields the equation which relates #x# and #y#:

#xy = 108#

Now, use this equation and substitute the second value of #y# in order to find its related value of #x#:

#xy = 108#

#x(-3) = 108#

#x = 108/(-3)#

#x = -36#