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Two researchers are studying the decline of orangutan populations. In one study, a population of 784 orangutans is expected to decrease at a rate of 25 orangutans per year. In a second study, the population of a group of 817 orangutans is expected to decrease at a rate of 36 per year. After how many years will the two populations be the same?

Verified Answer :

fundodobird

Step 1:
Set Variables (We will use x & y)

x = years
y = total orangutan population

Step 2:
Set up Equations

784 - 25x = y
817 - 36x = y

Step 3:
Set equations equal to each other & solve

784 - 25x = 817 - 36x
784 = 817 - 11x
-33 = -11x
3 years = x

Answer:

The answer is 3 years.

Step-by-step explanation:

Let the years be denoted by 't' ,when both populations will be same.

1st study says a population of 784 orangutans is expected to decrease at a rate of 25 orangutans per year.

Equation becomes:

\(y=784-25t\)

In a second study, the population of a group of 817 orangutans is expected to decrease at a rate of 36 per year.

Equation becomes:

\(y=817-36t\)

Now to solve for 't' we will equal both the equations.

\(784-25t=817-36t\)

\(36t-25t=817-784\)

\(11t=33\)

So, t = 3 years.

So, the answer is 3 years.

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