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Lesson Example Discussion Quiz: Class Homework

Step-3

Title: One Variable Data

Grade: 1400-a Lesson: S4-L1

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	The mean amount of time that the 20 employees of a construction company have worked for the company is 6.7 years. After one of the employees leaves the company, the mean amount of time that the remaining employees have worked for the company is reduced to 6.25 years. How many years did the employee who left the company work for the company?
2	Step	Given that the mean time worked by all 20 employees is 6.7 years, multiply the mean by the number of employees:	\$20 \times 6.7 \$ = 134 years
3	Step	After one employee leaves, the mean time worked by the remaining 19 employees is given as	6.25 years
4	Step	Multiply the new mean by the number of remaining employees:	\$ 19 \times 6.25\$ = 118.75 years
5	Step	Subtract the total time worked by the remaining employees from the initial total time worked by all 20 employees: This gives us the time worked by the employee who left the company	134 - 118.75 = 15.25 years
6	Step	The employee who left the company worked for 15.25 years.
7	Choice.A	This option suggests that the employee who left the company worked for 0.45 years. However, the total time worked by all 20 employees initially was 134 years, and the difference between the initial total time worked and the total time worked by the remaining 19 employees is 15.25 years. This option does not align with our calculations	0.45
8	Choice.B	This option proposes that the employee who left the company worked for 2.3 years. Similar to option A, this doesn’t align with our calculations based on the difference between the initial total time worked and the total time worked by the remaining employees	2.3
9	Choice.C	This option suggests that the employee who left the company worked for 9 years. However, our calculations show that the difference between the initial total time worked and the total time worked by the remaining employees is 15.25 years, which is greater than 9 years	9
10	Choice.D	This option proposes that the employee who left the company worked for 15.25 years. According to our calculations, the difference between the initial total time worked and the total time worked by the remaining employees is indeed 15.25 years, which aligns perfectly	15.25
11	Answer	Option	D
12	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

The mean amount of time that the 20 employees of a construction company have worked for the company is 6.7 years. After one of the employees leaves the company, the mean amount of time that the remaining employees have worked for the company is reduced to 6.25 years. How many years did the employee who left the company work for the company?

Step

Given that the mean time worked by all 20 employees is 6.7 years, multiply the mean by the number of employees:

\$20 \times 6.7 \$ = 134 years

Step

After one employee leaves, the mean time worked by the remaining 19 employees is given as

6.25 years

Step

Multiply the new mean by the number of remaining employees:

\$ 19 \times 6.25\$ = 118.75 years

Step

Subtract the total time worked by the remaining employees from the initial total time worked by all 20 employees:
This gives us the time worked by the employee who left the company

134 - 118.75 = 15.25 years

Step

The employee who left the company worked for 15.25 years.

Choice.A

This option suggests that the employee who left the company worked for 0.45 years. However, the total time worked by all 20 employees initially was 134 years, and the difference between the initial total time worked and the total time worked by the remaining 19 employees is 15.25 years. This option does not align with our calculations

0.45

Choice.B

This option proposes that the employee who left the company worked for 2.3 years. Similar to option A, this doesn’t align with our calculations based on the difference between the initial total time worked and the total time worked by the remaining employees

2.3

Choice.C

This option suggests that the employee who left the company worked for 9 years. However, our calculations show that the difference between the initial total time worked and the total time worked by the remaining employees is 15.25 years, which is greater than 9 years

Choice.D

This option proposes that the employee who left the company worked for 15.25 years. According to our calculations, the difference between the initial total time worked and the total time worked by the remaining employees is indeed 15.25 years, which aligns perfectly

15.25

Answer

Option

Sumup

Can you summarize what you’ve understood in the above steps?