barista alex is crafting a new coffee blend. he combines two coffee beans: bean a, which has a bitterness level of 25%, and bean b, which has a bitterness level of 75%. to create his signature blend, he wants a 1000g batch with a bitterness level of 40%. how much of each coffee bean should he use?

Answer:

Barista Alex should use 700g of bean A (with 25% bitterness) and 300g of bean B (with 75% bitterness) to create his 1000g batch with a bitterness level of 40%.

Step-by-step explanation:

To create a 1000g batch of coffee blend with a bitterness level of 40%, you can use a weighted average based on the bitterness levels of the two beans, bean A (25%) and bean B (75%).

Let x be the amount of bean A (with 25% bitterness) and y be the amount of bean B (with 75% bitterness) in the blend. You want the total batch to be 1000g, so we have:

x + y = 1000

Now, to achieve the desired bitterness level of 40%, you can set up the following equation based on the weighted average:

(25% * x + 75% * y) = 40% * 1000

Now, let's convert the percentages to decimal values (divide by 100):

(0.25x + 0.75y) = 0.40 * 1000

Simplify:

0.25x + 0.75y = 400

Now you have a system of two equations:

x + y = 1000

0.25x + 0.75y = 400

You can solve this system of equations. Let's use the substitution method. Solve equation (1) for x:

x = 1000 - y

Now, substitute this expression for x into equation (2):

0.25(1000 - y) + 0.75y = 400

Now, solve for y:

0.25 * 1000 - 0.25y + 0.75y = 400

0.75y - 0.25y = 400 - 250

0.5y = 150

y = 150 / 0.5

y = 300

So, he should use 300g of bean B (with 75% bitterness). Now, you can find the amount of bean A by using the first equation:

x + 300 = 1000

x = 1000 - 300

x = 700

Therefore, Barista Alex should use 700g of bean A (with 25% bitterness) and 300g of bean B (with 75% bitterness) to create his 1000g batch with a bitterness level of 40%.