a fair rate for piecework is 1.2 times the rate which lets a worker of average speed earn a living wage…

a fair rate for piecework is 1.2 times the rate which lets a worker of average speed earn a living wage. manuel is trying to determine a fair rate for piecework in his garment factory. there are 3 workers in the factory, one of whom produces 19 garments over the course of an hour, a second who produces 23 garments an hour, and the third of whom produces 30 garments per hour. (a) recall that an average (mean) is determined by adding the numbers and then dividing by the number of numbers. find the average number of garments per hour for the workers in the factory. mean: garments/hour (b) assume a living wage of $18.36/hour. divide the living wage by the average number of pieces to establish a base rate per item. round to the nearest cent. base rate per item: $ (c) multiply your answer to part (b) by 1.2 to establish a fair rate for each piece completed. round to the nearest cent. what is the fair rate for piecework in this factory? fair piecework rate: $ /item

a fair rate for piecework is 1.2 times the rate which lets a worker of average speed earn a living wage. manuel is trying to determine a fair rate for piecework in his garment factory. there are 3 workers in the factory, one of whom produces 19 garments over the course of an hour, a second who produces 23 garments an hour, and the third of whom produces 30 garments per hour. (a) recall that an average (mean) is determined by adding the numbers and then dividing by the number of numbers. find the average number of garments per hour for the workers in the factory. mean: garments/hour (b) assume a living wage of $18.36/hour. divide the living wage by the average number of pieces to establish a base rate per item. round to the nearest cent. base rate per item: $ (c) multiply your answer to part (b) by 1.2 to establish a fair rate for each piece completed. round to the nearest cent. what is the fair rate for piecework in this factory? fair piecework rate: $ /item

Answer

Explanation:

Step1: Calculate the mean of garments per hour

The number of garments per hour are 19, 23, and 30. The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 3$, $x_1=19$, $x_2 = 23$, $x_3=30$. So $\bar{x}=\frac{19 + 23+30}{3}=\frac{72}{3}=24$ garments/hour.

Step2: Calculate the base - rate per item

The living wage is $18.36$ per hour. Divide the living wage by the average number of pieces. The base - rate per item $r_1=\frac{18.36}{24}=0.765\approx0.77$ dollars per item.

Step3: Calculate the fair piece - work rate

Multiply the base - rate per item by 1.2. The fair piece - work rate $r_2=r_1\times1.2$. Substitute $r_1 = 0.77$ into the formula, $r_2=0.77\times1.2 = 0.924\approx0.92$ dollars per item.

Answer:

(a) 24 garments/hour (b) $0.77 (c) $0.92