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
25r=80; 200 residents were surveyed.
Start Fraction 2 over 5 End Fraction r equals 80 ; 200 residents were surveyed.
52r=80; 200 residents were surveyed.
Start Fraction 5 over 2 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.
80r=25; 200 residents were surveyed.
Start Fraction 2 over 5 End Fraction r equals 80 ; 200 residents were surveyed.
The equation that represents the number of residents surveyed is: Start Fraction 2 over 5 End Fraction r equals 80.
To find the number of residents surveyed, we can solve this equation. Multiply both sides of the equation by 5/2 to isolate 'r':
Start Fraction 2 over 5 End Fraction r * Start Fraction 5 over 2 End Fraction equals 80 * Start Fraction 5 over 2 End Fraction
This simplifies to:
r = (80 * 5) / 2
r = 400 / 2
r = 200
Therefore, 200 residents were surveyed.
To find the equation representing the number of residents surveyed, we need to set up a proportion based on the information given.
The proportion is:
(2/5)r = 80
Now, to solve for r, we can multiply both sides of the equation by the reciprocal of 2/5, which is 5/2:
(5/2) * (2/5)r = (5/2) * 80
r = 200
Therefore, the equation representing the number of residents surveyed is (2/5)r = 80, and 200 residents were surveyed.
So, the correct option is:
Start Fraction 2 over 5 End Fraction r equals 80; 200 residents were surveyed.