SOLUTION: Stella's catering is planning a wedding reception. The bride and groom would like to serve a nut mixture containing 25% peanuts. Stella has available mixtures that are either 40% o

Question 160573: Stella's catering is planning a wedding reception. The bride and groom would like to serve a nut mixture containing 25% peanuts. Stella has available mixtures that are either 40% or 10% peanuts. How much of each type should be mixed to get a 10-lb mixture that is 25% peanuts?
Found 2 solutions by KnightOwlTutor, ptaylor:
Answer by KnightOwlTutor(293) (Show Source): You can put this solution on YOUR website!
The total quantity is 10lbs. This amount never changes only the composition.
X=# lbs of 40%peanuts
10-x==# lbs of 10%peanuts
Convert % to decimal format=40%=.4, 10%=.1 25%=.25
The linear equation is as follows" .40x+.1(10-x)=10(.25)
To make it easier multiply each term by a hundred. It doesn't change the equation it just makes it easier to solve.
40x+(10)(10-x)=10(25)
Use the distributive propery
40x+100-10x=250
Subtract 10x from 40x
30x+100=250
Subtract 100 from both sides of the equation
30x=150
divide both sides by 30
x=5
5lbs of 40% peanuts are needed
10-5=5lbs of 10% peanuts are needed
To double check your answer you plug in the values in the above equation
40x+(10)(10-x)=10(25)
.4(5)+.1(5)=10(.25)
2.+.5=2.5

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of 40% peanuts needed
Then 10-x=amount of 10% peanuts needed
Amount of pure peanuts in the 40% mixture (0.40x) plus amount of pure peanuts in the 10% mixture ((0.10(10-x)) has to equal amount of pure peanuts in final mixture(0.25*10). So, our equation to solve is:
0.40x+0.10(10-x)=0.25*10 get rid of parens
0.40x+1-0.10x=2.5 subtract 1 from each side
0.40x-0.10x+1-1=2.5-1 collect like terms
0.30x=1.5 divide each side by 0.30
x=5 lb----------------------------------amount of 40% peanuts needed
10-x=10-5=5 lb---------------amount of 10% peanuts needed
CK
0.40*5+0.10*5=0.25*10
2+0.5=2.5
2.5=2.5
Hope this helps---ptaylor
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