SOLUTION: How many pounds of raisins worth $1.50 per pound must be mixed with 10 pounds of peanuts worth $1.20 per pound to produce a mixture worth $1.40 per pound? Give an numerical answer

Question 785255: How many pounds of raisins worth $1.50 per pound must be mixed with 10 pounds of peanuts worth $1.20 per pound to produce a mixture worth $1.40 per pound?
Give an numerical answer ONLY.
Answer by wilft1(217) (Show Source): You can put this solution on YOUR website!
this is going to require 2 equations
first one is going to be r + p = 10 (raisins plus peanuts equals 10 pounds)
our second equation is going to be 1.5r + 1.2p = 1.4 ( $1.50 per pound of raisins added to $1.20 per poind of peanuts will equal our $1.40 mixture)
we are going to do this using the subtraction method
r + p = 10
1.5r + 1.2p = 1.4
multiply our 1.4 by 10
r + p = 10
1.5r + 1.2p = 14
we want to get rid of the decimal points, so multiply both sides of the bottom equation by 10
r + p = 10
15r + 12p = 140
we want to eliminate one of the variables, so lets multiply the top equation by -12 to get rid of p
-12r + -12p = -120
15r + 12p = 140
add up the two equations
3r = 20
divide both sides by 3
r = 6.66
now tht we know the value of r, plug it in to find the value of p
15(6.66) + 12p = 140
99.9 + 12p = 140
subtract 99.9 from both sides
12p = 40.1
divide both sides by 12
p = 3.34
we now have both our values. you will need 6.66 pounds of raisins and 3.34 pounds of peanuts to have 10 pounds worth $1.40 per pound
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