SOLUTION: How many pounds of a chicken feed that sells for $5 a lb. must be mixed with 400 pounds of a feed that sells for $8 a lb.to make a chicken feed that sells for $7.50 a lb.? 5x+8x/4

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Question 789692: How many pounds of a chicken feed that sells for $5 a lb. must be mixed with 400 pounds of a feed
that sells for $8 a lb.to make a chicken feed that sells for $7.50 a lb.? 5x+8x/400=7.50
Answer by josgarithmetic(39616) (Show Source):
You can put this solution on YOUR website!
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.

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 .

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, being equivalent to , which would be . (Generalizing here so you see the rule).