Question 740881
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If the snack mix is made of sea monster scales, which cost $3.50 per pound, and baby whale barnacles, 
which cost $5 per pound, how many pounds of sea monster scales will she need to create s 45 pound blend 
that's worth $4.50 per pound ?
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Take x pounds of the $3.50 ingredient per pound and (45-x) pounds of the $5 ingredient per pound.

The blend will cost  3.50x + 5*(45-x) dollars for 45 pounds.


Equate it to the cost of 45 pounds of the blend at $4.50 per pound

    3.50x + 5*(45-x) = 45*4.50  dollars.


Simplify this equation and find x

    3.50x + 5*45 - 5x = 45*4.50,

    3.50x - 5x = 45*4.50 - 5*45,

       -1.50x  = 45*(4.50-5)

       -1.50x  = 45*(-0.5)

            x  = {{{(45*0.5)/1.50}}} = {{{45/3}}} = 15.


<U>ANSWER</U>.  15 pounds of the monster scale at $3.50  should be mixed with  45-15 = 30 pounds of the baby shale barnacles at $5 per pound.


<U>CHECK</U>.  We will check the price of the blend per pound  {{{(15*3.50 + 30*5)/(15+30)}}} = 4.50 dollars per pound of the blend.  ! correct !
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Solved and checked.