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%.
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%.