SOLUTION: 1st question- If four times a number added to 3 is divided by the number plus 8, the result is seven halves. find the number. ----------- ----------- ----------- ----------- ----

Question 292028: 1st question- If four times a number added to 3 is divided by the number plus 8, the result is seven halves. find the number.
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2nd question- One custodian cleans a suite of offices in 5 hours. When a second worker is asked to join the regular custodian, the job takes only 2 1/2 hours. How long does it take the second worker to do the same job alone?
thank you
Found 2 solutions by texttutoring, richwmiller:
Answer by texttutoring(324) (Show Source): You can put this solution on YOUR website!
If four times a number added to 3 is divided by the number plus 8, the result is seven halves. find the number.
Let's break it down in parts.
4 times a number: 4x
added to 3: 4x+3
Divided by the number plus 8: (4x+3)/(x+8)
And it's equal to 7 halves, or 7/2
Putting it all together:

First multiply both sides by x+8.

Then multiply both sides by 2. (this is called cross-multiply)

8x+6=7x+56
x=50

For your second question,
the first custodian's rate = 1 suite/5 hours
the second custodian's rate = x suites/5 hours
their combined rate of work = 1 suite/2.5 hours
(First custodian's work rate) + (second custodian's work rate) = combined work rate
1/5 + x/5 = 1/2.5
Rearrange this for x and you'll find that x=1, meaning that the second custodian's work rate is the same as the first's, 1 suite/5 hours. It would take him the same amount of time as the first custodian.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
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