A question about percentages.

Question

$ 6 \text{ kg} $ if a salt solution contains $ 40\% $ of salt by weight. How many kilogram of salt must be added to obtain a solution containing $ 60\% $ of salt by weight?

I have trouble understanding how to solve this.

60% of salt by weight means that

$60\% \cdot 6 = 3.6 \text{ kg} $

So I need $ 3.6 \text{ kg} $ of salt in the solution to have $ 60\% $ of salt by weight.

This means I need to add $ 1.2 \text{ kg} $ of salt more to have $ 60\% $ of salt by weight?

I believe my thinking process is wrong. Can I get some help. Thanks in advance!

Answer 1

If $x$kg salt is added,

the ratio will be $$\dfrac{6\cdot40\%+x}{6+x}$$ which needs to be $$=60\%$$

Answer 2

Some simpler thought.

Firstly, we can calculate the weight of the salt. Analyzing the first sentence, we have:

In $100$ kg of solution there are $40$kg of salt.

In $6$ kg of solution there are $x$ kg of salt.

Solving the equation: $$\frac{100}{6} = \frac{40}{x}\implies x = 2.4.$$ Thus, there are $2.4$ kg of salt in our initial solution.

Now, we need to increase the amount of the salt by $x$ kg, such that the percentage of salt is $60\%$. So, analyzing that in 2 sentences, we have:

In $100$ kg of solution, there are (we want) $60$ kg of salt.

In $(6+x)$ kg of solution, there are $(2.4+x)$ kg of salt.

Thus: $$ \frac{100}{6+x} = \frac{60}{2.4+x}$$

Solving for $x$ gives us the amount of salt we need to add.

Answer 3

Initially your solution contains $2.4$ kg of salt. Let $x$ kg be added so that resulting ...

so you have now $ 60 $ percent of $( 6 + x) = 2.4 + x $ which on solving gives x = 3 kg