Question

3. If the lab technician needs 30 liters of a 25% acid solution, how many liters of the 10% and the 30% acid solutions should she mix to get what she needs?

Answer 1

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The answer is 7.5% of 10 liter acid and 22.5 liters of 30% is required to make 30 liters of 25% acid.

Step-by-step explanation:

Let there be x liters of 10% acid solution and y liters of 30% acid solution.

So, we can write the equation as:

x + y = 30

or  

y = 30 - x

x liters of 10% solution and y liters of 30% solution will add up to give 30 liters of 25% acid solution.  

We can set up another equation as:

x liters of 10% acid + y liters of 30% acid = 30 liters of 25% acid

Changing percentage to decimals:

0.1(x) + 0.3(y) = 0.25(30)

By putting the values we get

0.1x + 0.3(30-x) = 7.5

0.1x + 9 - 0.3x = 7.5

- 0.2x = - 1.5

x = 7.5 liters

y = 30 - x = 30 - 7.5 = 22.5 liters

Thus 7.5% of 10 liter acid and 22.5 liters of 30% is required to make 30 liters of 25% acid.

Answer 2

Answer:

let , x liters of the 10% and y liters of the the 30% acid solutions is needed

If the lab technician needs 30 liters of a 25% acid solution

the acid in the solution = 30×25/100liters =7.5 liters

so,

$x + y = 30...................(1)$

$\frac{x}{10} + \frac{3y}{10} = 7.5...............(2)$

$(2) \times 10 - ( 1). \: we \: get$

$x + 3y = 75$

$x \: + y \: = 30$

( - ). ( - ). ( - )

...............................................

$2y =45$

$y =22.5$

$from \: (1) \: we \: get$

$x = 30 - 22. 5= 7.5$