Question 1114099
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The solution by tutor stanbon is fine.  But let me suggest a couple of alternative solution processes that you might find easier for you to use.<br>
The formal definition of inverse variation applied to this problem says
{{{W = k/L}}}
where W is the weight that can be supported, L is the length of the beam, and k is some constant.<br>
In the solution by stanbon, you use the given information to find the constant k; then you use that value to find the weight that can be supported by the longer beam.<br>
For me, it is easier to find the answer without specifically solving for the constant k.<br>
To do that, I prefer to think of inverse variation for this problem as
{{{W*L = k}}}.<br>
Since the product of weight and length is a constant, to solve the problem I just do
{{{800*10 = x*16}}}
{{{8000 = 16x}}}
{{{x = 500}}}<br>
An even faster path to the solution is possible if you think of inverse variation as meaning that if one of the variables is multiplied by a factor of n, then the other number needs to get divided by that same factor.<br>
Applied to this problem, I simply see that the new length is 8/5 times the original; that means the weight that can be supported is 5/8 as much:
{{{800*(5/8) = 500}}}