Question 789692
Pay closer attention to cost and pounds.  This is a mixture problem and the concentration is DOLLARS per POUND.  Your target is 7.50 dollars per pound.


Using the variable choices as you tried,
x = pounds of the lower priced feed
y = pounds of the higher priced feed, but you do NOT need this as variable.


Already you were given to start with 400 pounds of the 8$/pound feed.

{{{highlight((5x+8*400)/(x+400)=7.50)}}}
SOLVE FOR x.




SOME INSTRUCTION---------------------------------------------


DEVELOP THE EQUATION:


{COST OF MIXTURE}/{AMOUNT OF MIXTURE}={PRICE FOR MIXTURE}


You know the amount of the $8/pound chicken feed, 400 pounds.
The amount of the $5/pound feed is unknown variable, x.
Cost for the mixture is 5x+8*400 dollars.


The amount of mixture is a variable expression, x+400.


You want the PRICE of the mixture to be 7.50 dollars per pound.


Put this altogether and make {{{(5x+8*400)/(x+400)=7.50}}}.


You clear the "fraction" by doing something to BOTH sides of the equation.  This means, multiply left and right sides by (x+400); simplify if you wish.  You are initially relying on the idea, {{{n/d=c}}} being equivalent to {{{(n/d)(d)=cd}}}, which would be {{{n=cd}}}.   (Generalizing here so you see the rule).