SOLUTION: I am trying to help my daughter with Algebra, but it's been SO long... Here are two questions. I think if she can get the hang of it, she will take off. She is super-smart! Serg

Question 351330: I am trying to help my daughter with Algebra, but it's been SO long... Here are two questions. I think if she can get the hang of it, she will take off. She is super-smart!
Sergio sells a mixture of Virginia peanuts and Spanish peanuts for $3.40 per pound. To make the mixture, he uses Virginia peanuts that cost $3.50 per pound and Spanish peanuts that cost $3.00 per pound. He mixes 10 pounds at a time. How many pounds of Virginia peanuts does he use?
and,
A pineapple drink contains 15 percent pineapple juice. How much pure pineapple juice should be added to 8 quarts of the pineapple drink to obtain a mixture containing 50 percent juice?
If you just want to pick one, that is fine. Thanks SO much! My e-mail is NordicStrength@aol.com
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Sergio sells a mixture of Virginia peanuts and Spanish peanuts for $3.40 per pound.
To make the mixture, he uses Virginia peanuts that cost $3.50 per pound and
Spanish peanuts that cost $3.00 per pound.
He mixes 10 pounds at a time.
How many pounds of Virginia peanuts does he use?
:
This is a typical mixture problem, this method can be used for most of them:
Let x = amt $3.50 nuts required (Virginia)
then
(10-x) = amt of $3 nuts required
:
3.5x + 3(10-x) = 3.4(10)
3.5x + 30 - 3x = 34
3.5x - 3x = 34 - 30
.5x = 4
x =
x = 8 lb of Virginia nuts required
:
:
Confirm this (10 - 8 = 2 lb of Sp nuts)
3.5(8) + 3(2) = 3.4(10)
28 + 6 = 34
:
:
A pineapple drink contains 15 percent pineapple juice.
How much pure pineapple juice should be added to 8 quarts of the pineapple
drink to obtain a mixture containing 50 percent juice?
:
Let x = amt of pure p.a juice
The resulting amt = (x+8)
:
.15(8) + 1x = .5(x+8)
1.2 + x = .5x + 4
x - .5x = 4 - 1.2
.5x = 2.8
x =
x = 5.6 qts of pure p.a. juice required
:
:
Check this
.15(8) + 5.6 = .5(13.6)
1.2 + 5.6 = 6.8; confirms our solution
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