I'm having trouble with a word problem. It is a Number Problem, You have $30 in
change in your drawer, consisting of dimes and quarters. write an inequity that
shows the different number of coins in your drawer. I honestly do do not know
even where to begin. Please Help.

There must be some quarters among your $30 in change, for if there were no
quarters, and all were dimes (300 of them), your $30 wouldn't consist of dimes
AND QUARTERS, but only of dimes.

The most dimes you could have would be when you have the least possible number
of quarters.

You can't have just one quarter because that would leave $29.75 to have all in
dimes, and you can't have that because you would need a nickel, but you don't
have any nickels!

But you can have as few as two quarters, because that would leave $29.50 which
you could have with 295 dimes.

So the least number of quarters you could have would be 2 and the most number
of dimes you could have is 295

Therefore if D represents the number of dimes, then D is less than or equal to
295, so the way to write that as an inequality is

               D < 295

and if Q represents the number of quarters, then since there must be at least
two quarters, the way to write that as an inequality is

               Q > 2


Now we'll go the other way:

There must be some dimes among your $30 in change, for if there were no dimes,
and all were quarters (120 of them), your $30 wouldn't consist of dimes and
quarters, but only of quarters.

The most quarters you could have would be when you have the least possible
number of dimes.

You can't have just one dime because that would leave $29.90 and you can't have
that all in quarters. Neither can you have $29.80, nor $29.70, nor $29.60 only
in quarters. However you can have $29.50 with 118 quarters (which means you
must have at least 5 dimes). 

Therefore the least number of dimes you can have is 5 and the most number of
quarters you can have is 118.

Therefore since Q represents the number of quarters, then Q is less than or
equal to 118, so the way to write that as an inequality is

               Q < 118

and since D represents the number of dimes, then since there must be at least 5
dimes, the way to write that as an inequality is

               D > 5

Putting all the inequalities together:

               D < 295
               Q > 2
               Q < 118
               D > 5

Turn the 2nd and 4th inequalities backward, so they'll all be "less than
or equal"'s
               D < 295
               2 < Q
               Q < 118
               5 < D

Now we can combine the 4th and 1st of these with D in 
the middle as

             5 < D < 295
               
We can combine the 2nd and 3rd with Q in the middle as

             2 < Q < 118

Edwin