Question 224039
The manager of a specialty food store combined almonds that cost $4.50 per pound with walnuts that cost $2.50 per pound. How many pounds of each were used to make a 100-pound mixture that costs $3.24 per pound?


Step 1.  Let {{{x}}} be the number of pounds of almonds.


Step 2.  Let {{{100-x}}} be the number of pounds of walnuts since we have a 100-pound mixture.


Step 3.  Let {{{4.50x}}} be the dollar value of almonds.


Step 4.  Let {{{2.50(100-x)}}} be the dollar value of walnuts.


Step 5.  Let {{{4.50x+2.50(100-x)=3.24*100}}} for a one-hundred pound mixture.


Step 6.  Solve the equation {{{4.50x+2.50(100-x)=3.24(100)}}} using the following steps


*[invoke explain_simplification "4.50x+2.50(100-x)=3.24(100)" ]


With x=37 and 100-x=63, check dollar value...4.50*37+2.50*63=324 dollars for a 100 pound mixture which is a true statement.


Step 7.  ANSWER:  The amount of almonds is 37 pounds and the amount of walnuts is 63 pounds.


I hope the above steps and explanation were helpful. 


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