the manager of a coffee shop has one of coffee that sells for $6 per lb and another type that sells for $11 per lb.the manager wishes to mix 70lbs of the $11 coffee to get a mixture that will sell for $8 per lb. how many pounds of the $6 coffee should be used.

Question

amistre64 · Answer

amount@$6 = 70(11-8)/(8-6) i think ...

anonymous · Answer

i a getting good at these

amistre64 · Answer

dbl chk 105 @ 6 :)

anonymous · Answer

put x = amount of $6 beans.  then the total amount of beans will be 70 + x and you want that to cost $8 so the total cost will be 
$$8(70+x)$$ that is one side of the equation.  the other way to compute total cost is 
$$6x+70\times 11=6x+770$$

anonymous · Answer

so we have two expressions for total cost.  set them equal and solve.  should have 
$$6x+770=8(70+x)$$ and i'll be damned if we don't get 105

anonymous · Answer

now i gotta figure out how sensei got it in one step, and i had to find an equation

anonymous · Answer

I had 87.5 at first but 105 was my second,thanks

anonymous · Answer

yw

anonymous · Answer

ok sensei what is your trick here?

anonymous · Answer

or must i figure it out for myself?

anonymous · Answer

i mean i see that solving my equation amounts to exactly the same thing.  i am wondering if there is easy reasoning.

amistre64 · Answer

my trick is to work it our in general and then add the specifics :)

a+b = t; b = t-a

ax + by = tz

(t-b)x +by = tz

tx -bx +by = tz

b(y-x) = t(z-x)

b@y = t(z-x)/(y-x) where; t=total; z=final; x=other; and y= ...well, y

anonymous · Answer

ok fine. my way is easier

amistre64 · Answer

amount@$6 = 70(11-8)/(8-6) ... is another method; if I dont swap y and x I get the negative of it and can toss the sign

anonymous · Answer

i see what happened. you did all the algebra first that i would have to do second, so it is really the same.

amistre64 · Answer

exactly :)

amistre64 · Answer

so instead of hacking thru the same info time and again, I just use the general and fill in the blanks :)