Blending coffee?

Question

I don't have the answe so I don't know if I got it right! I got 15 pounds of $5 coffee.

A coffee house has 20lbs of a coffee that sells for $4 a lb. How many pounds of a coffee that sells for $8/lb should be mixed with the 20lbs of $4-per-lb coffee to obtain a blend that will sell for $5 per pound? How much of the $5 per pound coffee is there to sell?

Answer 1

(Weight) × ($ per lb.) = (Total $)
cheap: 20 · $4 = $80 worth of cheap coffee
expensive: (x) · $8 = $8x worth of expensive coffee

The weight of the blended coffee is 20 lbs. of cheap + x lbs. of expensive.
The total value of the blended coffee is $80 cheap + $8x expensive.
(Weight) × ($ per lb.) = (Total $)
blended: (x + 20) · $5 = $80 + $8x

5(x + 20) = 8x + 80
5x + 100 = 8x + 80
20 = 3x
x = (20 / 3) lbs. of expensive $8 coffee, or 6 2/3 lbs.
(x + 20) = 26 2/3 lbs. of blended $5 coffee.

Answer 2

Suppose we use x pounds of the $8 coffee. Then

20*4 + 8x = 5(20 + x)
80 + 8x = 100 + 5x
3x = 20
x = 20/3 = 6 2/3 lbs.

Altogether, you'll have 26 2/3 lbs. of $5 coffee to sell.

Answer 3

OK. You know you have 20lbs of 4$ coffee. To get y amount of a 5$ coffee you use ALL of the 4$ coffee and and x amount of 8$ coffee. That gives you the first equation:

20*4+8x=5y (eq1)

The sum of the volume of 4$ coffee (20) and 8$ coffee (x) will be the total volume of 5$ coffee (y) thus:

y=20+x (eq2)

Solve by inserting eq2 into eq1 ====>

20*4+8x=(20+x)5 simplified ===> 80+8x=100+5x
simplified by getting the x's on left side ===> 8x-5x=100-80
3x=20 ===> x=20/3 (eq3)

Now put your x-value from eq3 into eq2 to get y. y=20+x=20+20/3

Answer: You need to add 20/3 lbs of the 8$ coffee. You will then have 60/3 lbs of the 5$ coffee to sell.

Hope this is fairly easy to follow.

Answer 4

Since you are using up the 20lb of $4 coffee, this will dictate how much of the $5 coffee you will end up with.

You have 20lb of $4 coffee.
You have xlb of $8 coffee.

One eight of a lb of the $8 coffee will cost $1.

So for 20lb of the $4 coffee you mix 2∙5lb of the $8 coffee (1/8*20).

20lb of $4 coffee
+ 2.5lb of $8 coffee
--------------------------
= 22.5lb of $5 coffee.

Price: 22∙5 * 5 = $112.5

Answer 5

i dont know y but i keep getting 16 lbs. i kept using a chemistry equation oops thats my fav subject but now that i did it algebriacally i got 26.667 i always do that

Answer 6

Sorry! Dont know!