Question 227979
Almonds sell for $4.00 a pound, and pecans sell for $2.50 a pound. How many pounds of almonds must be mixed with 15 pounds of pecans, to produce a mixture sell for $3.50 a pound?


Step 1.  Let x be the amount of almonds sold.


Step 2.  Let x+15 the total amount of almonds and pecans mixture.


Step 3.  Let 4x be the dollar amount of almonds.


Step 4.  Let 15*2.50=37.50 be the dollar of pecans.


Step 5.  Let 4x+37.50 be the total dollar amount of pecans and almonds.


Step 6.  Let 3.50(x+15) be also the total dollar amount of pecans and almonds at $3.50 per pound.


Step 7.  Then, 4x+37.50=3.50(x+15) since Steps 5 and 6 are equal.


Step 8.  Solving the equation in Step 7 yields the following steps:


{{{4x+37.50=3.50x+52.50}}}


Add -3.50x-37.50 to both sides of the equation


{{{4x+37.50-3.50x-37.50=3.50x+52.50-3.50x-37.50}}}


{{{0.50x=15}}}


Divide 0.50 to both sides of the equation


{{{0.50x/0.50=15/0.50}}}


{{{x=30}}}


Check dollar value in Step 5:  30*4+37.50=157.50


Check dollar value in Step 6:  (30+15)*3.50=157.50  


So the dollar values are the same in Steps 5 and 6.


Step 9.  ANSWER:  The amount of almonds is 30 pounds.


I hope the above steps were helpful.


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Respectfully,
Dr J

http://www.FreedomUniversity.TV