Question

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?

Answer 1

He needs to drain about 78 grams of 25% acid solution

Further explanation

Order of Operations in Mathematics follow this following rule :

1. Parentheses
2. Exponents
3. Multiplication and Division
4. Addition and Subtraction

This rule is known as the PEMDAS method.

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.

Let us tackle the problem !

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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

Answer 2

this can be solved by establishing system of eqution:

let x be the amount of 25 % acid soln needs to be drained

y is the amount of 70% acid solution

first equation:

(100 – x) + y  = 100

Second equation

0.25(100 – x ) + 0.7y = 0.60(100)

Solving the system of equation

X = 77.78 g of 25 % acid solution is needed to be drained