Eric’s Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Eric $5.75 per pound, and type B coffee costs $4.50 per pound. This month’s blend used twice as many pounds of B coffee as type A, for a total cost of $309.75. How many pounds of type A were used?
Let's say Eric used x pounds of type A coffee.
Since he used twice as many pounds of type B coffee, then he used 2x pounds of type B coffee.
The total cost of the blend is $309.75, so we can write an equation based on the cost:
5.75x + 4.5(2x) = 309.75
Now we can solve for x:
5.75x + 9x = 309.75
14.75x = 309.75
x = 21
Therefore, Eric used 21 pounds of type A coffee in the blend.
Let's assume the weight of type A coffee used is "x" pounds.
According to the given information, the weight of type B coffee used is twice the weight of type A coffee, which is 2x pounds.
The cost of type A coffee is $5.75 per pound, so the total cost of type A coffee used is 5.75x dollars.
The cost of type B coffee is $4.50 per pound, so the total cost of type B coffee used is 4.50 * 2x = 9x dollars.
The total cost of both types of coffee used is $309.75, so we can write the equation as: 5.75x + 9x = 309.75.
Combining the like terms, we get: 14.75x = 309.75.
Dividing both sides by 14.75, we get: x = 309.75 / 14.75.
Simplifying the expression, we get: x = 21.
Therefore, 21 pounds of type A coffee were used in the blend.