Question 1202416
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Formally, inverse variation is defined as {{{y=k/x}}} where k is a constant.<br>
In practice, it is usually easier to work a problem involving inverse variation using the equivalent form {{{xy=k}}}<br>
In this problem, reds (r) vary inversely as yellows squared (y^2).  We need to find the number of reds when the number of yellows is 5, given that there are 100 yellows when there are 10 reds:<br>
{{{(10)(100^2)=x(5^2)}}}
{{{(10)(100)(100)=25x}}}
{{{x=10(100)(4)=4000}}}<br>
If your mental arithmetic is good, you can that answer quickly without using the formal formula.  The number of yellows is reduced from 100 to 5, a reduction by a factor of 20, so the number of reds is increased by a factor of 20^2=400; the new number of reds is 10*400 = 4000.<br>
ANSWER: 4000<br>