Okay, for these two questions I have the answers - but I can't figure out the process. HOW did they get these answers?
1. There are 132 members of the Volunteer Fire Dept. At a recent alarm, 1/4 of the volunteers responded. How many volunteers did NOT respond?
Answer: 99
2. It takes a machine 2 minutes and 15 seconds to assemble one chair. If the machine runs continuously for 6 hours, how many chairs will it produce?
Answer: 160
I need to know how to get these answers so that when I come to similar problems, I'll know. Thanks in advance.
1.
1/4 * 132 = 33
132 - 33 = 99
2.
Since 15 seconds is 1/4 of a minute, first change 2 minutes and 15 seconds to 2 1/4 minutes. Then, let's find out how many chairs are assembled in 60 minutes (1 hour).
60 / 2 1/4 = 60 / 9/4 = 60 * 4/9
60 * 4/9 = 240/9 = 26 2/3
Multiply: 26 2/3 * 6 = 160
4/217
Sure! Let's break down each question and explain the process to get the answers.
1. There are 132 members of the Volunteer Fire Dept. At a recent alarm, 1/4 of the volunteers responded. How many volunteers did NOT respond?
To find out how many volunteers did NOT respond, we first need to determine how many volunteers responded to the alarm. To do that, we'll multiply the total number of volunteers by the fraction that responded.
Total volunteers: 132
Fraction that responded: 1/4
To find the number of volunteers that responded, we'll multiply 132 by 1/4:
132 * 1/4 = 33
So, 33 volunteers responded to the alarm. To find out the number of volunteers that did NOT respond, we subtract the number of volunteers that responded from the total number of volunteers.
Total volunteers: 132
Volunteers that responded: 33
To find the number of volunteers that did NOT respond: 132 - 33 = 99
Therefore, 99 volunteers did NOT respond to the alarm.
2. It takes a machine 2 minutes and 15 seconds to assemble one chair. If the machine runs continuously for 6 hours, how many chairs will it produce?
To find out how many chairs the machine will produce, we need to determine the number of chairs produced in one duration of time and then multiply it by the number of durations the machine runs.
First, we need to convert the time taken to assemble one chair into minutes. Since there are 60 seconds in a minute, 2 minutes and 15 seconds can be expressed as 2 + (15/60) minutes.
Time taken to assemble one chair: 2 minutes + (15/60) minutes = 2.25 minutes
Next, we need to find the number of chairs produced in one duration of time by dividing the total duration by the time taken to assemble one chair.
Total duration: 6 hours
Time taken to assemble one chair: 2.25 minutes
To find the chairs produced in one duration:
(6 * 60) / 2.25 = 160
So, the machine will produce 160 chairs if it runs continuously for 6 hours.
I hope this explanation helps you understand the process to get these answers! Let me know if you have any further questions.