Question

The coffee merchant in mixed a coffee called Mississippi mud with a coffee called Pennsylvania pitch black to create a new coffee called Texas T if you mix some of the mud which cost $1.50 per pound with 6 pounds of pitch black which cost two dollars per pound to get his batch of Texas T which cost $1.80 per pound how many pounds of mud did he use

Answer 1

4 pounds of mud

Explanation:

Let the mud be added as
`x` pounds.

Given:

Cost of 1 pound of mud = $ 1.50

∴ Cost of
`x` pounds of mud =
`1.5x`

Cost of 1 pound of pitch black = $ 2

∴ Cost of 6 pounds of pitch black =
`2* 6=\$ 12`

Amount of Texas T made =
`x+6` pounds.

Cost of 1 pound of Texas T = $ 1.80

∴ Cost of
`x+6` pounds of Texas T =
`1.80(x+6)`

Now, cost of Texas T will be equal to the sum of cost of mud and pitch black. This gives,

`1.80(x+6)=1.5x+12\\1.8x+10.8=1.5x+12\\1.8x-1.5x=12-10.8\\0.3x=1.2\\x=(1.2)/(0.3)=4`

Therefore, he used 4 pounds of mud coffee.