I need to solve as an equation. A coffee merchant has coffee beans that sell for $9 per pound and $12 per pound. The two types are to be mixed to create 100 lb of a mixture that will sell for $11.25 per pound. How much of each type of been should be used in the mixture?

Question

I need to solve as an equation. A coffee merchant has coffee beans that sell for $9 per pound and $12 per pound. The two types are to be mixed to create 100 lb of a mixture that will sell for $11.25 per pound. How much of each type of been should be used in the mixture?

Assume 1 lb of mix contains x lb of the $9 coffee and 1-x lb of the $12 coffee.
9 x + 12 (1-x) = 11.25
0.75 = 3x
x = 0.25 (25% $9 coffee and 75% $12 coffee.

Answer 1

To solve this problem, we can set up an equation based on the information given. Let's assume that 1 pound of the mixture contains x pounds of the $9 coffee and 1-x pounds of the $12 coffee.

Now, we know that the mixture will contain a total of 100 pounds, so we can set up the equation:

9x + 12(1-x) = 11.25

Now, let's solve this equation step by step:

9x + 12 - 12x = 11.25

Combining like terms:

-3x + 12 = 11.25

Subtracting 12 from both sides:

-3x = -0.75

Dividing both sides by -3:

x = 0.25

So, x represents the amount of the $9 coffee in the mixture. Since 1 pound of the mixture contains x pounds of the $9 coffee, we have 0.25 pounds or 25% of the $9 coffee.

Similarly, 1-x represents the amount of the $12 coffee in the mixture. Therefore, we have 1-0.25 = 0.75 pounds or 75% of the $12 coffee.

In conclusion, to create a 100-pound mixture that sells for $11.25 per pound, you should use 25% (or 0.25 pounds) of the $9 coffee and 75% (or 0.75 pounds) of the $12 coffee.