Please help

Question

A store mixes brazilian coffee worth $11 per kilogram and Turkish coffee worth $13 per kilogram. The mixture is to sell for $12 per kilogram. Find how much of each should be used to make a 360 kilogram mixture 

Answer 1

Hi Mishorita;

quantity of Brazilian....x kg

quantity of Turkish....(360-x)kg

[($11/kg)(x kg)]+[($13/kg)(360-x)(kg)]=($12/kg)(360 kg)

The unit of kilograms is in the denominators and numerators of all facets of the equation.  It cancels...

$11x+$13(360-x)=$12(360)

The unit of dollars is in the numerator of all facets of the equation.  It cancels...

11x+13(360-x)=12(360)

Now that all units are aligned, we may calculate...

11x+4680-13x=4320

4680-2x=4320

Let's subtract 4680 from both sides...

4680-4680-2x=4320-4680

-2x=-360

Let's divide both sides by -2...

(-2x)/-2=-360/-2

x=180

(360-x)=180

We need 180 kg of each type of coffee.

 

Answer 2

Let x= the fraction of the cheap coffee and y be the fraction of the expensive stuff then x+y =1 so y=1-x and 

 

11x+13(1-x)= 12 want the cost of the mixture to be $12/kg

 

11x-13x+13=12

 

-2x=12-13=-1

 

x=1/2  and y=1/2 so you would need 180kg of each

 

Regards

Jim