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
80r=2/5; 200 residents were surveyed.
80 r equals Start Fraction 2 over 5 End Fraction ; 200 residents were surveyed.
2/5r=80; 200 residents were surveyed.
Start Fraction 2 over 5 End Fraction r equals 80 ; 200 residents were surveyed.
2/5r=80; 32 residents were surveyed.
Start Fraction 2 over 5 End Fraction r equals 80 ; 32 residents were surveyed.
5/2r=80; 200 residents were surveyed.
Start Fraction 5 over 2 End Fraction r equals 80 ; 200 residents were surveyed.
Start Fraction 2 over 5 End Fraction r equals 80 ; 200 residents were surveyed.
The correct equation representing the number of residents surveyed is 80r = 2/5. To find out how many residents were surveyed, we can solve this equation.
To isolate r, we can divide both sides of the equation by 80:
80r/80 = (2/5) / 80
Simplifying, we get:
r = (2/5) / 80
To divide by a fraction, we can multiply by the reciprocal:
r = (2/5) * (1/80)
Multiplying the numerators and denominators, we have:
r = 2/400
Simplifying, we get:
r = 1/200
This means that one resident is represented by 1/200 of the surveyed population.
To find the total number of residents surveyed, we can divide the total number of respondents (80) by the fraction representing one resident:
Total residents surveyed = 80 / (1/200)
To divide fractions, we can multiply by the reciprocal:
Total residents surveyed = 80 * (200/1)
Multiplying the numerators and denominators, we get:
Total residents surveyed = 80 * 200
Calculating, we find that:
Total residents surveyed = 16,000
Therefore, 16,000 residents were surveyed.
The correct equation that represents the number of residents surveyed is 2/5r = 80.
To solve for the number of residents surveyed, we need to isolate the variable "r" on one side of the equation.
To do this, we can divide both sides of the equation by 2/5:
(2/5r)/(2/5) = 80/(2/5)
Simplifying, we get:
r = 80 / (2/5)
To divide by a fraction, we can multiply by its reciprocal:
r = 80 * (5/2)
Multiplying, we get:
r = 400 / 2
Simplifying further, we find that:
r = 200
So, 200 residents were surveyed.
Therefore, the correct answer is: 2/5r = 80; 200 residents were surveyed.