A survey of n people in the town of Eros found that 50% of them preferred…
2023
A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another survey of 100 people in the town of Angie found that 60% preferred Brand A. In total, 55% of all the people surveyed together preferred Brand A. What is the total number of people surveyed ?
- A.
50
- B.
100
- C.
150
- D.
200
Attempted by 29 students.
Show answer & explanation
Correct answer: D
Solution:
Let n be the number of people surveyed in the town of Eros.
Number who prefer Brand A in Eros = 50% of n = n/2.
Number who prefer Brand A in Angie = 60% of 100 = 60.
Total people surveyed = n + 100. Total who prefer Brand A = n/2 + 60, which equals 55% of the combined total:
Set up the equation: n/2 + 60 = 0.55(n + 100).
Solve: n/2 + 60 = 0.55n + 55 → 60 − 55 = 0.55n − 0.5n → 5 = 0.05n → n = 100.
Total surveyed = n + 100 = 100 + 100 = 200.
Answer: 200 people