To determine how many grams of a 12% salt solution can be made using all the salt from a 20% salt solution, we first need to calculate how much salt is contained in the original solution.
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Calculate the amount of salt in the 20% solution: \[ \text{Amount of salt} = \text{Total solution} \times \text{Concentration} \] \[ \text{Amount of salt} = 180 , \text{grams} \times 0.20 = 36 , \text{grams} \]
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Now, we want to find out how much 12% salt solution can be made with 36 grams of salt: Let \( x \) be the total mass of the new 12% salt solution we want to create.
The amount of salt in this new solution can be expressed as: \[ \text{Salt in new solution} = x \times 0.12 \]
Since we know we have 36 grams of salt, we can set up the equation: \[ 0.12x = 36 \]
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Solving for \( x \): \[ x = \frac{36}{0.12} = 300 , \text{grams} \]
Therefore, you can make 300 grams of a 12% salt solution using all the salt contained in the original 20% salt solution.