SOLUTION: 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?

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?
Answer by drj(1380) (Show Source): You can put this solution on YOUR website!
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:

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

Divide 0.50 to both sides of the equation

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.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV

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