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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

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Answer:

4 pounds of mud

Step-by-step explanation:

Let the mud be added as [tex]x[/tex] pounds.

Given:

Cost of 1 pound of mud = $ 1.50

∴ Cost of [tex]x[/tex] pounds of mud = [tex]1.5x[/tex]

Cost of 1 pound of pitch black = $ 2

∴ Cost of 6 pounds of pitch black = [tex]2\times 6=\$ 12[/tex]

Amount of Texas T made = [tex]x+6[/tex] pounds.

Cost of 1 pound of Texas T = $ 1.80

∴ Cost of [tex]x+6[/tex] pounds of Texas T = [tex]1.80(x+6)[/tex]

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

[tex]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=\frac{1.2}{0.3}=4[/tex]

Therefore, he used 4 pounds of mud coffee.

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