Question

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

Answer 1

To solve this kind of problem,  there are two concepts: the total amount of solution and the total amount of acid

in this case, suppose there are x grams of the 25% solution, y grams of the 70% of soltuion
x + y = 100                             => y= 100-x
0.25x + 0.7y =0.6 *100  =60
replace y with 100-x:   0.25x + 0.7(100-x)=60
                                     0.45x=10
                                            x= 22.22
100-22.22=77.78
so he needs to drain about 77.78 grams of the solution. 

Answer 2

77.78 grams

Further explanation

Given:

A chemist has 100g of 25% acid solution.

Question:

How much of these solution he needs to drain and replace with 70% acid solution to obtain 100g of 60% acid solution?

The Process:

We will solve the chemical problem of mixed concentration. A chemist wants to get an acid solution with new concentrations. He needs to drain the initial solution and replace it with another concentration of an acid solution.

• Let x grams 25% acid solution mixed with y grams of 70% acid solution to obtain 100g of 60% acid solution.
• Remember, a chemist first had 100 grams of acid solution. Then the part he needs to drain is (100 - x) grams.

Let's arrange the equations.

$\boxed{ \ x + y = 100 \ grams \ } \rightarrow \boxed{ \ y = 100 - x \ } \ ....... (Equation-1)$

$\boxed{ \ \frac{(x \ grams)(25 \%) + (y \ grams)(70 \%)}{100 \ grams} = 60 \% \ } ....... (Equation-2)$

We work on Equation-2 first.

$\boxed{ \ 25x + 70y = 6000 \ } \rightarrow \boxed{ \ 5x + 14y = 1200 \ } \ ... (Equation-2)$

Substitute Equation-1 to Equation-2.

$\boxed{ \ 5x + 14(100 - x) = 1200 \ }$

$\boxed{ \ 5x + 1400 - 14x = 1200 \ }$

$\boxed{ \ 5x - 14x = 1200 - 1400 \ }$

$\boxed{ \ - 9x = -200 \ }$

Therefore, $\boxed{ \ x = 22.22 \ grams \ }$

Thus, he needs to drain $\boxed{\boxed{ \ 100 \ grams - 22.22 \ grams = 77.78 \ grams \ }}$

Learn more

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Keywords: a chemist, has 100g, 25% acid solution, how much, he needs, to drain, and replace with, 70%, to obtain, 60%, mixed, initial, new