```Question 351330
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 = {{{4/.5}}}
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 = {{{2.8/.5}}}
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```