Question 351536: Hello Masters in math, can you help me to solve my assignments in algebra
Regards,
JM- Philippines
Problem #1
The sum of three numbers is 138. The second is 5 more than the smallest and the third is 10 more than the smallest. Find the numbers.
Problem #2
The sum of three numbers is 49. The second number is three times the first number and the third number is 6 less than the first number. Find the three numbers.
Problem #3
Mr. Salvador can mow his lawn in 2 hours. His son Arnel, can do the same job in 3 hours. How long will it take them to do the job if they work together?
Problem #4
Three secretaries worked together typing a group of form letters. Melissa could have done them alone in 2 hours, Carol in 3 hours and Linda in 2 hours. How long did the secretaries need to type letters working together?
Problem #4
A tank can be filled by two pipes separately in 10 and 15 minutes respectively. When a third pipe is used simultaneously with the first two pipes, the tank can be filled in 4 minutes. How long would it take for the third pipe alone to fill the tank?
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Hello Student in math, here are the solutions in algebra
m.ananth@hotmail.ca
Problem #1
The sum of three numbers is 138. The second is 5 more than the smallest and the third is 10 more than the smallest. Find the numbers.
let smallest be x
second = x+5
third = x+10
x+x+5+x+10 = 138
3x+15 =138
3x=138-15
3x=123
x= 41 smallest number
46 second number
51 third number
Problem #2
The sum of three numbers is 49. The second number is three times the first number and the third number is 6 less than the first number. Find the three numbers.
let first number be x
second = 3x
third = x-6
...
x+3x+x-6 = 49
5x-6 =49
5x=55
x= 11 first number
second = 33
third = 5
Problem #3
Mr. Salvador can mow his lawn in 2 hours. His son Arnel, can do the same job in 3 hours. How long will it take them to do the job if they work together?
Salvador can do 1/2 job in 1 hour
Arnel can do 1/3 of the job in 1 hour
..
Together they will do 1/2 + 1/3 of the job in 1 hour
=5/6 of the job in 1 hour.
so they will take 6/5 hours
6/5 * 60 = 72 minutes OR 1 hour 12 minutes
Problem #4
Three secretaries worked together typing a group of form letters. Melissa could have done them alone in 2 hours, Carol in 3 hours and Linda in 2 hours. How long did the secretaries need to type letters working together?
...
Melissa can do 1/2 job in 1 hour
carol can fo 1/3 job in 1 hour
Linda can do 1/2 job in 1 hour
...
Together they will do 1/2 + 1/2 + 1/3 = 4/3 of the job in 1 hour
so they will take 3/4 hours to do the job.
Problem #4
A tank can be filled by two pipes separately in 10 and 15 minutes respectively. When a third pipe is used simultaneously with the first two pipes, the tank can be filled in 4 minutes. How long would it take for the third pipe alone to fill the tank?
one pipe can do 1/10 of the job in 1 minute
second pipe can do 1/15 of thejob in 1 minute
...
together they can do 1/10 +1/15 of the job in 1 minute
5/30 = 1/6 of the job in 1 minute.
...
All three do the job in 4 minutes
so they do 1/4 0f the job in 1 minute
1/4 - 1/6 = 1/12 of the job in 1 minute
So pipe three will take 12 minutes when used alone.
m.ananth@hotmail.ca
mananth@hotmail.com
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