A surgery is conducted in a curtain 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?
The equation that represents the number of residents surveyed is 2/5r = 80, where r is the total number of residents surveyed.
To solve for r, we can multiply both sides of the equation by 5/2:
(5/2)(2/5r) = (5/2)(80)
r = 200
Therefore, 200 residents were surveyed.
To represent the number of residents surveyed, we can use the equation:
r = (number of respondents / fraction of respondents who like the beach)
Given that two-fifths of the respondents, or 80 residents, said they like spending their vacation at the beach, the fraction of respondents who like the beach is 2/5.
Substituting the given values into the equation, we have:
r = (80 / 2/5)
To simplify, we can multiply the numerator by the reciprocal of the fraction:
r = 80 * (5/2)
Multiplying the numerator by the fraction, we get:
r = 400 / 2
Simplifying the division, we get:
r = 200
Therefore, a total of 200 residents were surveyed.
To find the equation that represents the number of residents surveyed, we can set up the following proportion:
(2/5) = 80/r
This proportion states that two-fifths of the total number of residents surveyed (r) is equal to 80. We can solve this equation to find the value of r.
To solve for r, we can cross-multiply:
2r = 5 * 80
2r = 400
Dividing both sides by 2:
r = 200
Therefore, the equation representing the number of residents surveyed is:
(2/5) = 80/200
To find the number of residents surveyed, we solve for r, which equals 200. So, 200 residents were surveyed.