Question 292028
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:

{{{(4x+3)/(x+8) = 7/2}}}


First multiply both sides by x+8.


{{{(4x+3) = 7(x+8)/2}}}


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

{{{2(4x+3) = 7(x+8)}}}

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.