Question

The manager of a bulk foods establishment sells a trail mix for $8 per pound and premium cashews for $15 per pound. The manager wishes to make a 105-pound trail mix-cashew mixture that will sell for $10 per pound. How many pounds of cashews should be used?

Answer 1

use this equation. .
(1) x+y=105

(2) x(8) +y(15)= 105(10)( x+y)

where x is the trail, while y is cashew

Answer 2

Removed my post, had a serious typo in equation. Jerwyn seems to have the solution, though I am not 100% sure on how to solve this one.

Answer 3

No biggie my friend

Answer 4

I don't see it either

Answer 5

so how many pound is it

Answer 6

thanks

Answer 7

I keep getting hung up on this problem for some reason

Answer 8

solve it using my equation given, i think substitution will do. . .

Answer 9

My original post had an 15 where there should have been a 10. Just removed it entirely since mine wasn't a complete solution anyway. Jerwyn, I don't understand that last (x+y) on the right hand side. Isn't the sum of the weights (105) already on that side?

Answer 10

@johncet. you must add (x+5) to the right side of the equation, because the asked is to 105 pounds which is 10 in cost and a mixed of trail and cashew.

Answer 11

from the statement "mixed trail and cashew". .

Answer 12

thanks fellows

Answer 13

Sure. I did some more work with this on paper. I do not understand where jerwyn got the (x+y), I think that is accidentally repeated. There is already an (x+y) where 105 is on that side of the equal sign. Maybe I am just not understanding it right. Anyhow, looking at his solution I see what I was missing the first time, that is the first equation, so it is a system of two equations.

x + y = 105
8x + 15y = (105)(10)

so: x = 105 - y

Plug into bottom equation...
8(105 -y) + 15y = (105)(10)
840 - 8y + 15y = 1050
7y = 210 .......... so y = 30

Plug y into first equation...
x + 30 = 105
So... x = 75

You can plug these into both equations to see that the weights add up to 105 pounds lie they should, and the costs add up to 1050 (or the cost of 105 pounds at $10 a pound).