Question 1154951
<br>
Without doing any detailed calculations, no -- your answer is not right.<br>
Your answer uses far more cashews than peanuts, so the price per pound should be much closer to $5.50 than it is to $2.30.  But $2.80 is much closer to $2.30 than it is to $5.50.<br>
A standard algebraic solution would go something like this....<br>
x = pounds of cashews at $5.50 per pound
0.5-x = pounds of peanuts at $2.30 per pound<br>
The combined mixture is a half pound worth $2.80 per pound:<br>
{{{x(5.5)+(0.5-x)(2.3) = 0.5(2.8)}}}<br>
You can finish solving the problem by that method if you want.  It is straightforward; but somewhat ugly, given all the decimals.<br>
Here is a solution using the method I like to use for solving mixture problems like this.<br>
(1) The target price per pound, $2.80, is 5/32 of the way from $2.30 to $5.50.  (Picture the three prices -- 2.30, 2.80, and 5.50 -- on a number line.  From 2.30 to 5.50 is 3.20; from 2.30 to 2.80 is 0.50.  2.80 is 0.50/3.20 = 5/32 of the way from 2.30 to 5.50.)<br>
That means 5/32 of the mixture is the more expensive cashews.<br>
ANSWER: (5/32) of the 1/2 pound mixture -- so 5/64 pounds -- are cashews;  the remaining 27/64 pounds are peanuts.<br>
CHECK:
{{{(5/64)(5.50)+(27/64)(2.30) = 1.40}}}
{{{(1/2)(2.80) = 1.40}}}<br>