<PRE><B>Question 551189</B>
i believe the implicit assumption in this problem is that the same amount of toys needs to be produced regardless of the number of elves working on them.
if there are 18 elves working and they each produce 20 toys each then the total production is 18 * 20 = 360 toys.
if 9 of them are sick then there are only 9 left to make 360 toys so each elf has to make 40 toys.
the inverse variation formula is y = k/x
y is the number of elves and x is the number of toys each produces.
we first solve for k using known facts.
when y = 18, x = 20 and the formula becomes:
18 = k / 20
solve for k to get k = 360.
when y is equal to 9, this formula now becomes:
9 = k / x
k is always equal to 360 so this formula now becomes:
9 = 360 / x
solve for x to get:
x = 360 / 9 = 40
with less elves working, each elf needs to produce more toys.
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