A merchant has 5 pounds of mixed nuts that cost $30. He wants to add peanuts that cost $1.50 per pound and cashews that cost $4.50 per pound to obtain 50 pounds of a mixture that costs $2.90 per pound. How many pounds of peanuts are needed?

Question

amistre64 · Answer

a + b = t
ax + by = tz

-ax -bx = -tx
  ax +by = tz
-------------
     b(y-x) = t(z-x)

b@y = t(z-x)/(y-x)

amistre64 · Answer

5 pounds of mixed nuts $30. ; what is this for?

(b)peanuts (y)$1.50 per pound 
cashews that cost (x)$4.50 per pound to obtain 

(t)50 pounds (z)$2.90 per pound. 

How many pounds of (b)peanuts are needed?

b@y = 50(2.90-4.50)/(1.50-4.50)

amistre64 · Answer

looks to be about 26 and 2/3

anonymous · Answer

ugh see im so confused how you got the equations

amistre64 · Answer

80/3 (1.5) + 70/3(4.5) = 50(2.9)
                           145  =  145

amistre64 · Answer

26 and 2/3 lbs of peanuts

amistre64 · Answer

the equations are standard for these types of problems; knowing what to fill in to the spots is the challange

anonymous · Answer

see i dont understand :( my teacher didnt explain it well and our whole class is lost

amistre64 · Answer

you know you need 2 different amounts; and they have to add up to a (t)otal of 50 lbs:

a + b = t ; 

you have prices to account for; a costs x much; b costs y much and when it is all said and done the (t)otal needs to cost z much

amistre64 · Answer

a + b = t
ax + by = tz

this is a system of eqatuons where a and b have to be the same amount and we can find them quite readily

whpalmer4 · Answer

End result is 50 lbs of nuts at $2.90/lb = $145 total cost.  We've already got 5 lbs of nuts that cost $30, so the remaining 45 lbs must cost $145-$30 = $115.  That works out to an average cost of $115/45 per pound.  $1.50 * p + $4.50 * (1-p) = $115/45 (p being the fraction of a pound of the added nuts mixture that is peanuts, and 1-p being the fraction of a pound that is cashews).  If we solve that equation for p, we get p = 0.648.  Multiply that fraction by 45 pounds, and we see that we need 29.17 lbs of peanuts.   Checking our work, 29.17*1.5 + (45-29.17)*4.5 = $115.

amistre64 · Answer

we can either graph the lines the equation will produce; or i just eliminate a variable and solve for the remainingone

amistre64 · Answer

is that what that first part was saying?  hunh ,,,,,,

amistre64 · Answer

i couldnt figure out what the 5lbs at 30 had to do with anything :)

amistre64 · Answer

ida feed it to the hogs and made a new batch

anonymous · Answer

ugh i just give up none of this is making sense

anonymous · Answer

thanks it kind of makes sense now