Question 1069813
<pre>
The other tutors are correct, but I'll bet your 
teacher wants you to make a chart for mixture
problems. 

So begin by making this chart:


         | ounces |  percent   | ounces of | 
         |of nuts |(as decimal)|  PECANS  |
---------|--------|------------------------|
 1st mix |        |            |           |
 2nd mix |        |            |           | 
---------|--------|------------|-----------|
final mix|        |            |           |
</pre>
She wants to use 25 ounces more of the second mixture
than the first.
<pre>
Let x = the number of ounces of the 1st mix.
Then x+25 = the number of ounces of the 2nd mix.
Fill those in

         | ounces |  percent   | ounces of | 
         |of nuts |(as decimal)|  PECANS  |
---------|--------|------------------------|
 1st mix |   x    |            |           |
 2nd mix |  x+25  |            |           | 
---------|--------|------------|-----------|
final mix|        |            |           |

Fill in the three percents expressed as decimals (hundredths)

         | ounces |  percent   | ounces of | 
         |of nuts |(as decimal)|  PECANS  |
---------|--------|------------------------|
 1st mix |   x    |    0.30    |           |
 2nd mix |  x+25  |    0.40    |           | 
---------|--------|------------|-----------|
final mix|        |    0.38    |           |

Add the number of ounces of 1st and 2nd mixes to get the
total number of ounces of final mix.
 x + x+25 = 2x+25.  So fill that in for the ounces of
final mix:

         | ounces |  percent   | ounces of | 
         |of nuts |(as decimal)|  PECANS  |
---------|--------|------------------------|
 1st mix |   x    |    0.30    |           |
 2nd mix |  x+25  |    0.40    |           | 
---------|--------|------------|-----------|
final mix| 2x+25  |    0.38    |           |

Next we fill in the last column with PECANs 
by taking the percentages of ounces of each of 
the three mixes.  So we just multiply the two 
columns:

         | ounces |  percent   | ounces of | 
         |of nuts |(as decimal)|  PECANS  |
---------|--------|------------------------|
 1st mix |   x    |    0.30    |0.30x      |
 2nd mix |  x+25  |    0.40    |0.40(x+25) | 
---------|--------|------------|-----------|
final mix| 2x+25  |    0.38    |0.38(2x+25)|           

The equation comes from adding up the ounces of PECANS
in 1st and 2nd mixes and setting it equal the the number
of ounces of PECANS in the final mix:

{{{matrix(1,7,

(matrix(7,1,ounces,of,PECANS,in,the,1st,mix)),
""+"",
(matrix(7,1,ounces,of,PECANS,in,the,2nd,mix)),
"",
""="",
"",
(matrix(7,1,ounces,of,PECANS,in,the,final,mix))
)}}}

0.30x + 0.40(x+25) = 0.38(2x+25)

Clear of decimals by moving them 2 places right:

    30x + 40(x+25) = 38(2x+25)

Solve that and get x = {{{25/3}}} or {{{8&1/3}}} 

Since we let x = the number of ounces of the 1st mix,
the number of ounces of the 30% mixture is {{{8&1/3}}} 

Since then x+25 = the number of ounces of the 2nd mix,
the number of ounces of the 40% mixture is {{{8&1/3+25=33&1/3}}}.

Edwin</pre>