Question 880195
<pre>
There are two ways to do these problems.
(1) using only 1 unknown
(2) using 2 unknowns.

I will assume you are studying using 2 unknowns.
If you have not gotten to using 2 unknowns yet,
then tell me in the thank you note and I'll show 
you how to do these using only one unknown.
</pre>
1. Ron has 30 coins with a total value of $5.25. 
The coins are dimes and quarters. How many of 
each coin does he have?
<pre>
             how        value of    value of 
             many        each         all
dimes         x           .10        .10x
quarters      y           .25        .25y
-----------------------------------------
totals       30                      5.25

          x+y=30                .10x+.25y=5.25 

Solve first equation for x
            x=30-y
Substitute in second equation
      .10(30-y)+.25y = 5.25    
      3.00-.10y+.25y = 5.25
           3.00+.15y = 5.25
                .15y = 2.25
                   y = 2.25/.15
                   y = 15 quarters

Substitute in x = 30-y
              x = 30-15
              x = 15 dimes  
                   
Checking: 15 quarters = $3.75
          15 dimes    =  1.50
                  total $5.25  
</pre>
2. Ron has 15 coins with a total value of $1.95. The 
coins are nickels and quarters. How many of each 
coin does he have?
<pre>
             how        value of    value of 
             many        each         all
nickels       x           .05        .05x
quarters      y           .25        .25y
-----------------------------------------
totals       15                      1.95

          x+y=15                .05x+.25y=1.95 

Same as above.  Get 9 nickels and 6 quarters

</pre>
3. How many liters of 80% alcohol solution and 20%
alcohol solution must be mixed to obtain 6 liters
of 40% alcohol solution?
<pre>
                                   how much
             how         percent     pure
             much        alcohol    alcohol 
            liquid       in each    in each        
stronger      x           .80        .80x
weaker        y           .20        .20y
-----------------------------------------
totals        6           .40       .40(6)

          x+y=6                .80x+.20y=.40(6)
                               .80x+.20y= 2.4

Same way, get x=2,  y=4

Edwin</pre>