Question

a detergent is created by mixing washing soda, borax, and water. the table below shows the composition of three different detergents.

composition of detergents

a
b
c
washing soda
0.05
0.15
0.20
water
0.80
0.80
0.70
borax
0.15
0.05
0.10

travis needs to use a combination of the detergents to create 100 ounces of a detergent that is 15% washing soda, 75% water, and 10% borax. which is true?

he will use equal parts of each detergent.
he will use more of detergent a than any other detergent.
he will use more of detergent b than any other detergent.
he will use more of detergent c than any other detergent.

Explanation:

Step1: Analyze the water content

Let the amounts of detergents \(A\), \(B\), and \(C\) be \(x\), \(y\), and \(z\) ounces respectively. We know \(x + y+z = 100\).
The water content equation: \(0.8x+0.8y + 0.7z=0.75\times100\).
Substitute \(z = 100-(x + y)\) into the water - content equation:

$$
LATEXBLOCK0
$$

Step2: Analyze the borax content

The borax - content equation: \(0.15x+0.05y + 0.1z=0.1\times100\).
Since \(z = 50\), we have \(0.15x+0.05y+0.1\times50 = 10\).
Substitute \(y = 50 - x\) (from \(x + y=50\)) into the borax - content equation:

$$
LATEXBLOCK1
$$

Answer:

He will use equal parts of each detergent.