A detergent is created by mixing washing soda, borax, and water. The table below shows the composition of three different detergents. Composition of Detergents ABCWashing Soda0.050.150.20Water0.800.800.70Borax0.150.050.10Travis 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?
Answer
A
He will use equal parts of each detergent.
B
He will use more of detergent A than any other detergent.
C
He will use more of detergent B than any other detergent.
D
He will use more of detergent C than any other detergent.
Explanation
Let the amounts of detergents A, B, and C be x, y, and z ounces. The water percentage gives 0.80(x + y) + 0.70z = 75, with x + y + z = 100; solving gives z = 50. The remaining 50 ounces must be split equally between A and B to reach 15% washing soda, so he uses 25 ounces each of A and B and 50 ounces of C. Therefore, he uses more detergent C than any other detergent.
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