Question 118506: 1. One half of a number is 3 more than one sisxth of the same number. What is the number?
2. The denominator of a certain fraction is three times the numerator. If one is added to the
numerator and subtracted from the denominator, the result equals 1/2. Find the original fraction.
3. The denominator of a fraction is 5 more than the numerator. If 5 is added to the numerator and 2 is added to the denominator, the value of the fraction is 8/9. Find the original fraction.
4. The numerator is one less than the denominator. If two is added to the denominator and
subtracted from the nomerator, the value of the fraction is 1/2. Find the original fraction.
5. Ed can do a job in four days. When Ed and Maymay work together, it would take them 2 1/3 days.
How long would the job take Maymay to do it alone?
6. A cold water faucet could fill a sink in 15 minutes, and a hot water faucet can fill it in 12
minutes. The drain can empty the sink in 25 minutes. If both faucet are on and the drain is open,
how long would it take to fill the sink?
7. Julius can paint a house three times faster than Ruben. Working together, they can paint a
house in four days. How long would it take the faster painter if he works alone?
Found 2 solutions by solver91311, ankor@dixie-net.com:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! It looks like you have put your entire homework assignment into one question. This site was not created so that you could get someone to do your homework for you. You have two different types of problems. I'll show you how to do one of each.
1. One half of a number is 3 more than one sixth of the same number. What is the number?
Let the number be x. One half of the number is then  . One sixth of the number is  and 3 more than that is  . So you can write:
Multiply both sides by 6 to eliminate the denominators:
Subtract x from both sides to get the variable on the left:
Divide both sides by 2:
Check your answer:
Half of  is 
One sixth of is 
 , answer checks
6. A cold water faucet could fill a sink in 15 minutes, and a hot water faucet can fill it in 12 minutes. The drain can empty the sink in 25 minutes. If both faucets are on and the drain is open, how long would it take to fill the sink?
If the cold faucet can fill the sink in 15 minutes, it fills  th of the sink in 1 minute. Likewise, the hot faucet fills  th of the sink in 1 minute. The LCD of 15 and 12 is 60, so the cold faucet fills the sink at  ths per minute, and the hot at  ths per minute. Together, they fill the sink at  ths per minute. Just as a sanity check, it would take 6 and 2/3 minutes to fill the sink IF the drain were CLOSED.
The drain empties the sink at  of the sink per minute. Now we need an LCD for 25 and 60:
 , so the LCD is 
With both faucets and the drain open fully, the sink is filling at a rate of  ths per minute minus  ths per minute, or  ths per minute.
The sink therefore fills in  minutes exactly, or 9 minutes as a very close approximation (rounded from the repeating decimal 9.09...). If you require a decimal answer (instead of a fraction), express it as 9 because you shouldn't give an answer that is more precise than the least precise measurement given in the problem. The time measurements given were all in whole minutes, so your answer should be in whole minutes.
By the way, remember the sanity check. 6 and 2/3 minutes to fill if the drain were closed and 9 minutes with the drain open is a ratio of about 1.4. 45/300 with the drain closed and 33/300 to fill with the drain open is also a ratio of about 1.4. That quick mental calculation assures us that the answer is reasonable.
Hope that helps.
John
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! 1. One half of a number is 3 more than one sixth of the same number. What is the number?
:
Let x = the number:
:
Just write what is says; (the word "is" usually means equal)
"One half of a number is 3 more than one sixth of the same number."
.5x = 3 +  x
Usually written like this:
.5x = x + 3
Multiply equation by 6 to get rid of the denominator
6(.5x) = 6*x + 6(3)
3x = x + 18
3x - x = 18
2x = 18
x = 18/2
x = 9
:
Check solution in the original equation:
.5(9) = 3 + *9
4.5 = 3 + 1.5, confirms out solution
:
:
2. The denominator of a certain fraction is three times the numerator. If one is
added to the numerator and subtracted from the denominator, the result equals
1/2. Find the original fraction.
:
Let x = the numerator:
It says,"The denominator of a certain fraction is three times the numerator."
Therefore: 3x = the denominator
:
It says,"If one is added to the numerator and subtracted from the denominator, the result equals 1/2."
 = 
:
Cross multiply and you have:
2(x + 1) = 1(3x - 1)
2x + 2 = 3x - 1
2 + 1 = 3x - 2x
x = 3
:
Check solution in original equation:
 = ; confirms our solution
:
:
In the next 2 problems, I will construct the equation and you can solve it.
If you have difficulty, you can email me for help.
:
3. The denominator of a fraction is 5 more than the numerator.
If 5 is added to the numerator and 2 is added to the denominator, the value of the fraction is 8/9.
 = 
Find the original fraction; (you can cross multiply here)
:
:
4. The numerator is one less than the denominator. If two is added to the denominator and subtracted from the numerator, the value of the fraction is 1/2. Find the original fraction.
:
Add 2 to the denominator and subtract 2 from the numerator
 =
Do the same here
:
:
5. Ed can do a job in four days. When Ed and May work together, it would take them 2 1/3 days.
:
Let x = time required for M to do the job alone
Let the completed job = 1
Use the decimal equiv of 1/3: 2.333 days
:
How long would the job take May to do it alone?
A simple equation:
 +  = 1
Multiply equation by 4x to get rid of the denominators, resulting in:
2.333x + 4(2.333) = 4x
9.333 = 4x - 2.333
9.333 = 1.67x
x = 9.333/1.667
x = 5.6 days, M's time working alone
:
Check solution in original equation
+  } =
.58325 + .4166 = .9998 ~ 1, confirms our solution
:
:
6. A cold water faucet could fill a sink in 15 minutes, and a hot water faucet
can fill it in 12 minutes. The drain can empty the sink in 25 minutes. If both
faucets are on and the drain is open, how long would it take to fill the sink?
:
Let x = time for this to take place
Let the full sink = 1
We have 3 elements here. Let filling be + and draining be neg
 +  -  = 1
We want to find a common multiple of all three denominators here
If we multiply the equation by that, it becomes pretty easy, doesn't it.
:
The best I can come up with is 15*12*25 = 4500
4500* + 4500* - 4500* = 4500(1)
cancel out the denominators and we have:
300x + 375x - 180x = 4500
I think that you can finish up this one now? (It won't be an even number)
:
:
7. Julius can paint a house three times faster than Ruben. Working together,
they can paint a house in four days. How long would it take the faster
painter if he works alone?
:
"J can paint a house 3 time faster than R"
We can take this to mean if J's time = x, then R's time is 3x
:
 +  = 1
Multiply equation by 3x:
3x* + 3x = 3x(1)
cancel out the denominators and we have:
3(4) + 4 = 3x
12 + 4 = 3x
3x = 16
x = 16/3
x = 5  days
:
Check our solution using x = 5.333 days
 +  =
.75 + .25 = 1; confirms our solution
:
:
Dear Student, I have taken a significant amount of time to show you how to do
these problems. Please, if you have question on what was done here, email me.
Your success in this is my main concern. A
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