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

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Question 181804: 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?
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
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?
:
let x and y be the amount of mixtures of 10% and 40% peanuts respectively
:
x+y=10..............eq 1
.10x+.4y=.25(10)....eq 2
:
rewrite eq 1 to highlight%28x%29=blue%2810-y%29 and plug that value into eq 2
:
.10(10-y)+.4y=2.5
:
1-.1y+.4y=2.5
:
.3y=1.5
:
highlight%28y=5%29pounds of 40% peanut mixture
:
highlight%28x%29=blue%2810-y=10-5%29=highlight%285%29pounds of 10% peanut mixture
:
we would expect an equal split since 25% is right in between 10% and 40%