SOLUTION: I have 2 whole chapters of word problems! Stella's Catering has nut mixtures that are either 10% or 40% peanuts. A wedding party wants a mixture that has 25% peanuts. How much of

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Question 1142752: I have 2 whole chapters of word problems!
Stella's Catering has nut mixtures that are either 10% or 40% peanuts. A wedding party wants a mixture that has 25% peanuts. How much of each type should be mixed in order to get a 10 lb mix of 25% peanuts?
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
L=10, low conc peanuts (%)
H=40, high conc peanuts
T=25, target conc.
M=10, pounds of nut mixture
v, unknown amount of the H percent peanut mixture
M-v, unknown amount of the L percent mix

highlight_green%28L%28M-v%29%2BHv=TM%29
Solve for v.

--
LM-Lv%2BHv=TM
Hv-Lv%2BLM=TM
v%28H-L%29%2BLM=TM
v%28H-L%29=TM-LM
v=%28TM-LM%29%2F%28H-L%29
highlight%28v=M%28%28T-L%29%2F%28H-L%29%29%29--------notice that upon substitution of givens, M is multiplied by what may be a fairly simple fraction.

ALSO notice that 25% is exactly in the middle of 10% and 40%.
Use 5 pounds of the 10% peanuts and use 5 pounds of the 40% peanuts.