Question

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?

Answer 1

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 2

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.