IXL | Estimate population size using proportions

Brittany is an avid birdwatcher and is trying to estimate the number of doves living in her region. She traps 29 doves and tags them. Later, she traps 420 doves, 14 of which are tagged. To the nearest whole number, what is the best estimate for the dove population?

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question

At the Museum of Natural History, there is a room filled with butterflies. Patrons can come into the room and watch the butterflies from close up. The butterfly caretaker, Aubrey, decides to approximate the population of the butterflies. She uses a net to capture 22 butterflies, marks them, releases them, and then later catches 800 butterflies. Of those 800 butterflies, 16 are marked. To the nearest whole number, what is the best estimate for the butterfly population?

solution

The ratio of marked butterflies to total butterflies should be about the same in both the sample population and the overall population. You know how many butterflies were in the sample and how many of those were marked. You also know the total number of marked butterflies.

Set up a proportion.

marked butterflies counted

total butterflies counted

total marked butterflies

estimated butterfly population

Plug in the numbers you know and solve for the butterfly population,

800

(

800

)

Multiply both sides by

800

(

800

)

Multiply both sides by

800

Simplify

800

Simplify

17,600

Simplify

Divide both sides by 16

1,100

Divide both sides by 16

The best estimate for the butterfly population is 1,100.

Looking for more? Try these:

Lesson: Proportions

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Teacher tools

Work it out

Not feeling ready yet? These can help:

L.12Solve proportions

L.11Do the ratios form a proportion: word problems

Lesson: Proportions

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