A coffee distributor needs to mix a(n) Tanzanian coffee blend that normally sells for $10.50 per pound with a Rift Valley coffee blend that normally sells for $12.00 per pound to create 70 pounds of a coffee that can sell for $10.99 per pound. How many pounds of each kind of coffee should they mix?

A coffee distributor needs to mix a(n) Tanzanian coffee blend that normally sells for $10.50 per pound with a Rift Valley coffee blend that normally sells for $12.00 per pound to create 70 pounds of a coffee that can sell for $10.99 per pound.

Now, to find the pounds of each kind of coffee they should mix.

Let the pounds of Tanzanian coffee be [tex]x.[/tex]

Let the pounds of Rift Valley coffee be [tex]y.[/tex]

So, total pounds of coffee is:

[tex]x+y=70[/tex]

[tex]x=70-y\ \ \ \ ........(1)[/tex]

Now, the total price of coffee per pound is:

[tex]10.50(x)+12.00(y)=10.99(70)[/tex]

[tex]10.5x+12y=769.3[/tex]

Substituting the value of [tex]x[/tex] from equation (1) we get:

[tex]10.5(70-y)+12y=769.3[/tex]

[tex]735-10.5y+12y=769.3[/tex]

[tex]735+2.5y=769.3[/tex]

Subtracting both sides by 735 we get:

[tex]2.5y=34.3[/tex]

Dividing both sides by 2.5 we get:

[tex]y=13.72.[/tex]

Rift Valley coffee = 13.72 pounds.

Now, substituting the value of [tex]y[/tex] in equation (1):

[tex]x=70-y\\x=70-13.72\\x=56.28.[/tex]

Tanzanian coffee = 56.28 pounds.

Therefore, they should mix 13.72 pounds of Rift Valley coffee and 56.28 pounds of Tanzanian coffee.