SOLUTION: 1. The number of workshop elves varies inversely with the number of toys produced. Eighteen elves make twenty Baby Wetsies each. - Write an equation that models the relationsh

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Question 551189: 1. The number of workshop elves varies inversely with the number of toys produced. Eighteen elves make twenty Baby Wetsies each.
- Write an equation that models the relationship between the number of elves working and the amount of toys each elf makes.
- Use the equation to calculate the amount of toys each elf produces when all but 9 elves are sick with the flu.
- Create a graph of the situation.
I am not understanding what to do with this math problem. I need help. Thanks.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
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.