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:
a 400
b 1,100
c 1,400
d 1,800

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 \(50\times0.78\).

$$50\times0.78 = 39$$

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

Multiply the number of non - purple candies in one box by 36.
Let \(N\) be the number of non - purple candies in 36 boxes.
\(N=39\times36\)

$$39\times36=(40 - 1)\times36=40\times36-36=1440 - 36 = 1404\approx1400$$

Answer:

C. \(1,400\)