find x when y = -5.

Question

y varies inversely with x. If y = 40 when x = 16, find x when y = -5.

Answer 1

If y varies inversely with x, then xy = k where k is the constant of variation.

Substituting, x = 16 and y = 40:

k = 16(40) = 640

To find x when y = -5, x = k/y = 640/(-5) = -128

Answer 2

if y varies inversely with x this means that either y is negative while x is positive and when x is negative y is positive. since y=40 and x=16 we need to establish some kind of relationship with x and y to make the inverse relationship true. Notice that 16 and 40 are related by the fact that their greatest common factor is 8 so 16 is 8 x 2 and 40 is 8 x 5 and one method two relate two numbers would be ratio which is a proportional relationship similar to a fraction. so from what we got before we can find that 16/40 or 2/5. Now that we have found the relations between these two numbers which are said to inversely vary we will find that if y=-5 which is a negative number and considering how negatives and positive numbers are opposite or inverse to each other and because we established a rational or fractional relationship between 16/40 which simplifies to 2/5 and due to y=-5 x will inversely by x=2 so the final answer is 2/-5 or just -2/5.