pre-algebra word problem: decrease in bees and hives

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sarah thorp

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An entomologist noted that in the past five years in the local forest preserve, the population of bees decreased by 35%. In her study, she recorded that the number of active hives five years ago was 35. If the number of active hives decreased at the same rate as the bee population, how many hives are there today?

Explain how you can use estimation in two different ways to help you with the answer.

The choices are A. 17 hives, B. 19 hives, C. 21 hives, and D. 23 hives
 
Hi Sarah, Welcome to the forums!

That's a fun word problem.
What have you done on your own, so far?

Lets think about this algebraically.
The total population and the total number of hives drop at the same rate.

So, we could write an equation that modeled this loss of bee population:
Current Population = Pop5YearsAgo - 35%(Pop5YearsAgo)

Now, if the population drop is proportional to the drop in hives, would it be fair to say that the hives dropped by 35% over those 5 years, as well?

If that is, in fact, a fair statement, then how could you substitute in your four multiple choice options into a similar equation (for number of hives) so that your equation (similar to the one I did above) is balanced?
 
Hey.

If the drop in bee population is proportional to the drop in number of hives, and after knowing that the bee population dropped 35% in 5 years, then total hive population would have to drop by 35% as well.

The choices are A. 17hives B. 19 hives C. 21 hives D. 23 hives

let hives = number of hives, 5 years ago:

Current Number of hives = hives - 0.35(hives)

Current Number of hives = 35 - 0.35(35) = 22.75 hives

which is approx equal to D.


Now how could you have used your multiple choice answer, D, to help you, (without knowing it was the correct answer)?

Think about going backwards from the steps we did above.
This is the only thing I can think of.
 
We're told that the bee population lost 35% of its population in 5 years. This says NOTHING about the rate at which it's decreasing; whether it's a constant or variable rate, we're not told. If it's a constant rate, the question should be easy. If it's variable, it might be slightly harder (as that could involve an exponential decay etc.).
 
We are told that bee population and number of hives drop at the same rate.

If the bee population drops 35% over 5 years, than the number of hives would have to drop by 35% (at the end of the five years), as well.

Five years ago there were 35 hives. 5 years later, the number of hives drops by 35%

If we wanted to, we could find this rate of decrease because we know the number of years it took to decrease 35%, but that would be unnecessary.

Keep it simple.
 
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