A Chemist has 100g of 25% acid solution. How much of these solution he needs to drain and replaced with 70% acid solution to obtain 100g of 60% acid solution?

In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.

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\(\texttt{ }\)

Given:

A Chemist has 100 g of 25% acid solution.

Let : The mass of the solution that need to be drained = x grams

\(\texttt{mass of acid from 25\% solution} = m_1 = 25\% \times (100-x) \texttt{ g}\)

\(\texttt{ }\)

x grams of 70% acid solution is added.

\(\texttt{mass of acid from 70\% solution} = m_2 = (70\% \times x) \texttt{ g}\)

\(\texttt{ }\)

Final solution → 100 g of 60% acid solution

\(\texttt{total mass of acid} = m_1 + m_2\)

\(60\% \times 100 = (25\% \times (100-x)) + (70\% \times x)\)

\(60 = 25 - 25\%x + 70\%x\)

\(60 - 25 = 45\%x\)

\(35 = 45\%x\)

\(x = 35 \div 45\%\)

\(x = 77\frac{7}{9} \texttt{ g}\)

\(x \approx 78 \texttt{ g}\)

\(\texttt{ }\)

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Answer details

Grade: Middle School

Subject: Mathematics

Chapter: Percentage

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent , cookies , chocolate , chip , paper , fourth , pieces , Number , 51 , 33 , 1/3