The proportion used to find the average number of trout you would expect to live in the pond is
[tex]\frac{7}{20}=\frac{x}{400}[/tex]
Solve the proportion to find the expected number of trout in the population.
The expected number of trout in the population is
$\square$
Answer (1)
Set up the proportion: 20 7 = 400 x .
Multiply both sides by 400 to isolate x : x = 20 7 × 400 .
Simplify the expression: x = 140 .
The expected number of trout in the population is 140 .
Explanation
Understanding the Problem We are given the proportion 20 7 = 400 x and asked to solve for x , which represents the expected number of trout in the population.
Isolating x To solve the proportion, we need to isolate x . We can do this by multiplying both sides of the equation by 400: x = 20 7 × 400
Calculating x Now we simplify the expression to find the value of x :
x = 20 7 × 400 x = 20 7 × 20 × 20 x = 7 × 20 x = 140 So, the expected number of trout in the population is 140.
Final Answer Therefore, the expected number of trout in the population is 140.
Examples
Imagine you are managing a fish farm and need to estimate the number of trout in a large pond. By taking a smaller sample and using proportions, you can estimate the total population size. For example, if you catch and count fish in a small section of the pond and find that 7 out of every 20 fish are trout, you can use this proportion to estimate the number of trout in the entire pond. This method is useful for managing resources and ensuring a healthy fish population.
