Question 87076
<pre>
You have at least $30 in change in your drawer,
consiting of dimes and quarters. Write an inequality 
that shows the different number of coins in your drawer.

.10d + .25q = 30

That may be all your teacher wants.

or

10d + 25q = 3000

Divide theough by 5

2d + 5q = 600

Maybe that's the form your teacher wants.

Or you can go further:

2d + (4q + q) = 600

2d + 4q + q = 600

Divide through by 2

d + 2q + {{{q/2}}} = 300

Isolate the fraction:

{{{q/2}}} = 300 - d - 2q

The right side is an integer A,
so the left side must equal integer A also

{{{q/2}}} = A ;  300 - d - 2q = A

q = 2A

Substitute:

300 - d - 2(2A) = A

300 - d - 4A = A

-d = 5A - 300

d = -5A + 300

d = 300 - 5A

d <u>></u> 0 so

300 - 5A <u>></u> 0
     -5A <u>></u> -300
       A <u><</u> 60

q = 2A

q <u>></u> 0 so

2A <u>></u> 0
 A <u>></u> 0

So 0 <u><</u> A <u><</u> 60

So you may choose A as any integer between 0 and 60
 
Then the number of dimes will be 300 - 5A and the
number of quarters will be 2A.

Edwin</pre>