SOLUTION: A company sells nuts in bulk quantities. When bought in bulk, peanuts sell for $1.40 per pound, almonds for $2.25 per pound, and cashews for $3.20 per pound. Suppose a specialty sh

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A company sells nuts in bulk quantities. When bought in bulk, peanuts sell for $1.40 per pound, almonds for $2.25 per pound, and cashews for $3.20 per pound. Suppose a specialty sh      Log On


   

Question 724475: A company sells nuts in bulk quantities. When bought in bulk, peanuts sell for $1.40 per pound, almonds for $2.25 per pound, and cashews for $3.20 per pound. Suppose a specialty shop wants a mixture of 450 pounds that will cost $2.73 per pound. Find the number of pounds of each type of nut if the sum of the number of pounds of almonds and cashews is four times the number of pounds of peanuts. Round your answers to the nearest pound.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Summary of data is like this:

p = pounds of peanuts, 1.40 $/#
a = pounds almosts, 2.25 $/#
c = pounds cashews, 3.20 $/#.
WANT 450 pounds mixture to cost $2.73/pound, and a%2Bc=4p

The sum of pound equation is p%2Ba%2Bc=450.
Because of the given "4p" relationship, this becomes p%2B4p=450, and so highlight%28p=90%29. We still have and will need to use, 90%2Ba%2Bc=450.

The mixture price equation is %281.4p%2B2.25a%2B3.2c%29%2F450=2.73, and with the p substitution and other steps, becomes
highlight%282.25a%2B3.2c=1102.5%29.

The much simpler system to solve for then is:
highlight%282.25a%2B3.2c=1102.5%29
highlight%2890%2Ba%2Bc=450%29
Solve for a and c. p is already solved.