For his science fair project, Seth is investigating the water quality in his school's water fountains. He finds that the water is safe to drink; a 50-milliliter water sample has just 13 milligrams of dissolved solids. If Seth fills a 2-liter bottle from one of the water fountains at his school, how many grams of dissolved solids would his bottle have?

Write your answer as a whole number, decimal, or simplified fraction. Do not round.
grams

1 answer

To find out how many grams of dissolved solids are in a 2-liter bottle filled from the water fountain, we first need to determine the concentration of dissolved solids in the water.

Seth's water sample of 50 milliliters contains 13 milligrams of dissolved solids.

First, let's convert the 2 liters to milliliters since the existing measurement is in milliliters.

\[ 2 \text{ liters} = 2000 \text{ milliliters} \]

Next, we can determine how many milligrams of dissolved solids are in 2000 milliliters of water by setting up a proportion based on the 50-milliliter sample:

\[ \text{Amount of dissolved solids in 2000 mL} = \left( \frac{13 \text{ mg}}{50 \text{ mL}} \right) \times 2000 \text{ mL} \]

Calculating the right side:

\[ \frac{13 \text{ mg}}{50 \text{ mL}} \times 2000 \text{ mL} = \frac{13 \times 2000}{50} \]

Now we can simplify \( \frac{2000}{50} \):

\[ \frac{2000}{50} = 40 \]

So:

\[ 13 \text{ mg} \times 40 = 520 \text{ mg} \]

Now, to convert milligrams to grams, we need to remember that:

\[ 1000 \text{ mg} = 1 \text{ g} \]

Therefore, to convert 520 mg to grams:

\[ 520 \text{ mg} = \frac{520}{1000} \text{ g} = 0.520 \text{ g} \]

Thus, the 2-liter bottle would have:

\[ \boxed{0.520} \text{ grams} \]