Question 939904
Do all as pounds and convert to ounces after solution of pounds is found.


Variables, a, r, p, for apples, raisins, peanuts


PRICES
Apples, 4.48
Raisins, 2.40
Peanuts, 3.44


Account for the price of mixture, $3.18/pound.
{{{(4.48a+2.40r+3.44p)/(a+r+p)=3.18}}}
{{{4.48a+2.40r+3.44p=3.18(a+r+p)}}}
{{{448a+240r+344p=318(a+r+p)}}}
{{{112a+60r+86p=79.5(a+r+p)}}}---not like this step
{{{224a+120r+172p=159(a+r+p)}}}
{{{(224-159)a+(120-159)r+(172-159)p=0}}}
{{{highlight_green(65a-39r+13p=0)}}}, one of the equations for the system.


Peanuts and Apples relationship:
{{{p/a=2}}}, meaning {{{highlight_green(p=2a)}}}, another equation for the system.


How much mixture?
ONE pound.
{{{highlight_green(a+r+p=1)}}}, now you have all the equations for the system.


Including coefficients of possible 0, or zero, and ordered first three columns as a, r, p, the system can be as this:
65a-39r+13p=0,2a-p=0,a+r+p=1
{{{system(65a-39r+13p=0,2a+0*r-p=0,a+r+p=1)}}}
That negative sign in the first equation seems unexpected.  I might have made a mistake in the work for that equation.


You can recheck, and then finish the solution process.


Notice also, the coefficients of the first equation are products of 13, so
{{{system(5a-3r+1p=0,2a+0*r-p=0,a+r+p=1)}}}