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.
25r=80; 32 residents were surveyed.
Start Fraction 2 over 5 End Fraction r equals 80 ; 32 residents were surveyed.
52r=80; 200 residents were surveyed.
Start Fraction 5 over 2 End Fraction r equals 80 ; 200 residents were surveyed.
80r=2/5; 200 residents were surveyed.
Start Fraction 2 over 5 End Fraction r equals 80 ; 200 residents were surveyed.
The correct equation that represents the number of residents surveyed is:
Start Fraction 2 over 5 End Fraction r equals 80.
To find out how many residents were surveyed, we can solve for r by multiplying both sides of the equation by the reciprocal of Start Fraction 2 over 5 End Fraction, which is Start Fraction 5 over 2 End Fraction.
Therefore, the number of residents surveyed, r, is:
r = Start Fraction 80 * Start Fraction 5 over 2 End Fraction End Fraction = <<80*(5/2)=200>>200
So, 200 residents were surveyed.
The equation that represents the number of residents surveyed is "2/5 r = 80". To find out how many residents were surveyed, we can solve this equation for r.
To solve for r, we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of 2/5, which is 5/2. This gives us:
(2/5 r) * (5/2) = 80 * (5/2)
Multiplying the numerator and denominator on the left side of the equation, and simplifying the right side, we get:
(r) * (1) = 400/2
r = 200
Therefore, 200 residents were surveyed. Thus, the correct option is "2/5 r = 80; 200 residents were surveyed."