Question

a box of fruit candy contains 50 candy pieces in five different colors: red, orange, yellow, green, and purple. willy opened the box and found that 22% of the candy pieces are purple. if the box willy opened is representative of that particular brand of fruit candy, which of the following best estimates the total number of non - purple candy pieces in 36 boxes of the same candy? choose 1 answer: 400 1,100 1,400

Explanation:

Step1: Calculate the number of non - purple candies in one box

The percentage of non - purple candies is \(100\% - 22\%=78\%\).
The number of candies in one box is \(n = 50\).
The number of non - purple candies in one box is \(50\times0.78\).

Step2: Calculate the number of non - purple candies in 36 boxes

The number of non - purple candies in 36 boxes is \(36\times50\times0.78\).
First, \(36\times50=(30 + 6)\times50=30\times50+6\times50 = 1500+300=1800\).
Then, \(1800\times0.78=(1800\times(0.8 - 0.02))=1800\times0.8-1800\times0.02=1440 - 36 = 1404\approx1400\).

Answer:

C. \(1,400\)