Question

One laundry detergent is 15% bleach and another is 40% bleach. How many ounces of each detergent must be used to make 48 ounces of a detergent that is 23% bleach?

Answer 1

32.64 ounces of a detergent that is 15% bleach was mixed with 15.36 ounces of a detergent that is 40% bleach to get 48 ounces of a detergent that is 23% bleach.

Explanation:

Let x be the amount of detergent in ounce of 15% bleach and let y be the amount of detergent in ounce of 40% bleach.

Since 48 ounces of detergent is made, hence:

x + y = 48 (1)

Also, 15% bleach detergent and 40% bleach detergent is mixed to make 48 ounces of a detergent that is 23% bleach, therefore:

0.15x + 0.4y = 0.23(48 ounce)

0.15x + 0.4y = 11.04 (2)

To find x and y, we solve equation 1 and equation 2 simultaneously by multiplying equation 1 by 0.15 and subtracting the result from equation 2:

0.25y = 3.84

y = 15.36 ounces

Put y = 15.36 in equation 1 to get:

x + 15.36 = 48

x = 48 - 15.36

x = 32.64 ounces

Therefore 32.64 ounces of a detergent that is 15% bleach was mixed with 15.36 ounces of a detergent that is 40% bleach to get 48 ounces of a detergent that is 23% bleach.