Question 136378
With these type of problems, you have to be able to explain
the reason for the formula, or chances are, you won't get
it right. I like to write the formulas out in words to see
if it makes sense. For this problem:
[(price/lb of peanuts)x(lbs of peanuts) 
+ (price/lb of cashews)x(lbs of cashews)] / (48 lbs of mixture) = $4/lb
This makes sense to me, because it's
($ + $)/ lbs = $/lb
Let {{{p}}} = pounds of peanuts in mixture
Let {{{c}}} = pounds of cashews in mixture
{{{(3p + 6c) / 48 = 4}}}
and
{{{p + c = 48}}}
{{{p = 48 - c}}}
Substitute this in the 1st equation
{{{(3(48-c) + 6c) / 48 = 4}}}
{{{(144 - 3c + 6c) / 48 = 4}}}
{{{144 + 3c = 4*48}}}
{{{3c = 192 - 144}}}
{{{3c = 48}}}
{{{c = 16}}}
and
{{{p = 48 - c}}}
{{{p = 48 - 16}}}
{{{p = 32}}}
The merchant needs 16 pounds of casews and 32 pounds of peanuts
check answer:
{{{(3p + 6c) / 48 = 4}}}
{{{(3*32 + 6*16) / 48 = 4}}}
{{{(96 + 96)/48 = 4}}}
{{{192/48 = 4}}}
{{{4 = 4}}}
OK
Remember, you must understand the formula you are using, or one little
change in the wording of the problem will throw you off