Question

A dental hygiene company is creating a new $24$ grams tube of toothpaste by combining two kinds of toothpaste, $A$ and $B$. $A$ contains $0.25\%$ of sodium fluoride as its active ingredient, and $B$ contains $0.30\%$ of triclosan as its active ingredients. The final product contains $6.9\%$ of the active ingrediemts from both the toothpastes. Solving which of the following systems of equations yields the number of grams of toothpaste $A\left(c\right)$ and the number of grams of toothpaste $B\left(b\right)$ that are mixed in the new toothpaste?

• A. $c+b=0.069,0.25c+0.3b=24$
• B. $c+b=24,0.0025c+0.003b=0.069$
• C. $c+b=24,0.025c+0.03b=0.069$
• D. $c+b=24,0.25c+0.3b=0.069$

Answer 1

Answer: (B)

$c+b=24,0.0025c+0.003b=0.069$

Solution:-

B

Start with the easier equation and use Process of Elimination.

The easier equation is related to the total number of ounces, $c+b$ in the tube.

According to the question, the tube has $24$ ounces, so $c+b=24$

Eliminate (A), since it does not include this equation.

The other equation in the set is related to the amount of active ingredients.

According to the question, c includes $0.25\%$ of sodium fluoride and b contains $0.30\%$ triclosan.

$0.25\%=0.0025$ and $0.30\%=0.003$

Therefore, in the correct equation, $c$ should be associated with $0.0025$ and $b$ should be associated with $0.003$.

Eliminate (C) and (D) because both of these equations get the percentages wrong.

The correct answer is (B).