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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[tex]\texttt{ }[/tex]

Given:

A Chemist has 100 g of 25% acid solution.

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

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

[tex]\texttt{ }[/tex]

x grams of 70% acid solution is added.

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

[tex]\texttt{ }[/tex]

Final solution → 100 g of 60% acid solution

[tex]\texttt{total mass of acid} = m_1 + m_2[/tex]

[tex]60\% \times 100 = (25\% \times (100-x)) + (70\% \times x)[/tex]

[tex]60 = 25 - 25\%x + 70\%x[/tex]

[tex]60 - 25 = 45\%x[/tex]

[tex]35 = 45\%x[/tex]

[tex]x = 35 \div 45\%[/tex]

[tex]x = 77\frac{7}{9} \texttt{ g}[/tex]

[tex]x \approx 78 \texttt{ g}[/tex]

[tex]\texttt{ }[/tex]

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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