A survey is conducted in a certain neighborhood to find out residents’ favorite vacation spot. Two-fifths of the respondents, or 80 residents, said they like spending their vacation at the beach. Which equation represents the number of residents, r , surveyed? How many residents were surveyed?(1 point)
The equation that represents the number of residents surveyed, r, is 5/2 * 80 = 200 residents surveyed. Answer: \boxed{r=200}.
To find the number of residents surveyed, we need to set up an equation. Let's call the total number of residents surveyed 'r'.
According to the information given, two-fifths of the residents surveyed (or 2/5 of r residents) said they like spending their vacation at the beach, which is equal to 80 residents.
So, the equation can be written as:
(2/5) * r = 80
To find the value of 'r', we can multiply both sides of the equation by 5/2 (or divide by 2/5), which cancels out the fraction:
r = 80 * (5/2)
r = 200
Therefore, the number of residents surveyed is 200.
To find the equation that represents the number of residents surveyed, we need to set up a proportion using the given information.
We are told that two-fifths (2/5) of the residents surveyed said they like spending their vacation at the beach, which is equal to 80 residents.
Let's represent the number of residents surveyed as 'r'. The proportion can be set up as:
(2/5) = 80/r
Now, we can solve this proportion to find the value of 'r', which represents the total number of residents surveyed.
To solve the proportion, we can cross-multiply:
2r = 5 * 80
2r = 400
Now, we can solve for 'r' by dividing both sides of the equation by 2:
r = 400/2
r = 200
Therefore, the equation that represents the number of residents surveyed is 2/5 = 80/r, and the total number of residents surveyed is 200.