SOLUTION: 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

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Question 740881: 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 thats worth $4.50 per pound
Found 4 solutions by lynnlo, ikleyn, josgarithmetic, greenestamps:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by ikleyn(53418) About Me  (Show Source):
You can put this solution on YOUR website!
.
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 ?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

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  = %2845%2A0.5%29%2F1.50 = 45%2F3 = 15.


ANSWER.  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.


CHECK.  We will check the price of the blend per pound  %2815%2A3.50+%2B+30%2A5%29%2F%2815%2B30%29 = 4.50 dollars per pound of the blend.  ! correct !

Solved and checked.



Answer by josgarithmetic(39701) About Me  (Show Source):
You can put this solution on YOUR website!
The given described information:

                         PRICE        POUNDS          COST
s. m. scales              3.50
b. w. barnackles          5.00         
mixture                   4.50          45               


                         PRICE        POUNDS          COST
s. m. scales              3.50         45-b          3.5(45-b)
b. w. barnackles          5.00           b            5b
mixture                   4.50          45           3.5(45-b)+5b

Relating cost per pound to the desired price
3.5%2845-b%29%2B5b=4.5%2A45
3.5%2A45-3.5b%2B5b=4.5%2A45
1.5b%2B3.5%2A45=4.5%2A45
1.5b=45
highlight%28b=30%29
30 pounds of baby whale barnacles, 15 pounds sea monster scales.

Answer by greenestamps(13258) About Me  (Show Source):
You can put this solution on YOUR website!


You have received two responses showing similar typical formal algebraic solutions to this 2-part mixture problem.

Here is a VERY short and quick solution using a method that can be used for any 2-part mixture problem like this. (The solution using this method is very quick for this example, because the numbers are "nice". But it can be used for any problem like this; the arithmetic just won't be so simple.)

Short solution: $4.50 is two-thirds of the way from $3.50 to $5.00, so 2/3 of the mixture must be the more expensive baby whale barnacles.

ANSWER: 30 pounds of baby whale barnacles and 15 pounds of sea monster scales.