how many kg of pure salt must be added to 30 kg of 2% solution of

Question

how many kg of pure salt must be added to 30 kg of 2% solution of salt and water to increase it to a 10% solution

 

please explain me details

Answer 1

Hi Amey,

 

Let's begin by writing expressions for the two input salt amounts and the final output salt amount:

    input pure salt amount:  (1.00)(x) 

    input 2% salt amount:  (0.02)(30)

    output 10% salt amount:  (0.10)(x + 30)

 

Next, let's write an equation to express the combining the two input salt amounts to produce the final output salt amount and then solve that equation for our unknown pure salt amount (x):

    (1.00)(x) + (0.02)(30) = (0.10)(x + 30)

    x + 0.6 = 0.1x + 3

    x - 0.1x = 3 - .6

    0.9x = 2.4

    x = 2.4/0.9

    x = 8/3 kg pure salt

        OR

 

     x = 2 and 2/3 kg pure salt

 

Finally, we can verify our answer by plugging it back into our equation and see if the input and output salt amounts are equal:

    (1.00)(x) + (0.02)(30) = (0.10)(x + 30)

    (1.00)(8/3) + (0.02)(30) = 0.10(8/3 + 30)

    8/3 + 0.6 = 0.8/3 + 3

    3(8/3) + 3(0.6) = 3(0.8/3) + 3(3)

    8 + 1.8 = 0.8 + 9

    9.8 kg salt = 9.8 kg salt

 

Since our combined input salt amounts equals our final output salt amount, we are confident that our answer is correct.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.

Answer 2

Let us mix x kg of pure salt. Pure means the concentration is 100%

so the mount of salt in the solution from here will be x kg.

Now total solution is 30+x kg. Amount of salt in this is 0.1(30+x)  (10% salt.)

the 30 kg salt solution has (.02)30 kg of salt in it ( 2% salt)

Our equation is

x+.02(30) = (30+x) ( 0.1)

x+0.6 =3+0.1x

0.9x = 2.4

x = 2.4/0.9 =2.67 kg.