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)
Responses
52r=80; 200 residents were surveyed.
Start Fraction 5 over 2 End Fraction r equals 80 ; 200 residents were surveyed.
80r=25; 200 residents were surveyed.
80 r equals Start Fraction 2 over 5 End Fraction ; 200 residents were surveyed.
25r=80; 200 residents were surveyed.
Start Fraction 2 over 5 End Fraction r equals 80 ; 200 residents were surveyed.
25r=80; 32 residents were surveyed.
Start Fraction 2 over 5 End Fraction r equals 80 ; 32 residents were surveyed.
The correct equation is 80r = 25. This means that 80 residents said they like spending their vacation at the beach, and r represents the total number of residents surveyed. To find the number of residents surveyed, we need to solve for r.
Dividing both sides of the equation by 80, we get:
r = 25/80
Simplifying the fraction, we get:
r = 5/16
Therefore, the number of residents surveyed is 5/16 of 80:
5/16 * 80 = 200/16 = 25.
So, 25 residents were surveyed.
The correct answer is: 25r = 80; 25 residents were surveyed.
The equation that represents the number of residents surveyed, r, is "Start Fraction 5 over 2 End Fraction r equals 80." Therefore, 200 residents were surveyed.
To solve this problem, we can use a proportion to find the total number of residents surveyed.
The given information states that two-fifths of the respondents, or 80 residents, said they liked spending their vacation at the beach. This can be represented by the equation:
(2/5) * r = 80
Here, 'r' represents the total number of residents surveyed, and (2/5) represents the fraction of residents who like spending their vacation at the beach.
To solve for 'r', we can multiply both sides of the equation by the reciprocal of (2/5), which is (5/2):
r = (80) * (5/2)
Simplifying this expression, we get:
r = 200
Therefore, the equation representing the number of residents surveyed is (2/5) * r = 80, and the number of residents surveyed is 200.