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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.
gram

1 answer

To find out how many grams of dissolved solids are in a 2-liter bottle of water based on the information provided, we can use the ratio from the 50-milliliter sample.

First, we know that:

  • The sample has 13 milligrams of dissolved solids in 50 milliliters of water.

Next, we need to calculate the amount of dissolved solids per liter. Since 1 liter is 1000 milliliters, we find the amount in 1 liter using the following steps:

  1. Find how many 50-milliliter portions are in 1 liter: \[ \frac{1000 \text{ mL}}{50 \text{ mL}} = 20 \]

  2. Calculate the total dissolved solids in 1 liter: \[ 20 \times 13 \text{ mg} = 260 \text{ mg} \]

Now, we want to find out how many grams of dissolved solids there are in 2 liters. Since we found that there are 260 milligrams in 1 liter, we multiply by 2:

\[ 260 \text{ mg} \times 2 = 520 \text{ mg} \]

  1. Convert milligrams to grams: Since there are 1000 milligrams in 1 gram, we convert the total: \[ \frac{520 \text{ mg}}{1000} = 0.520 \text{ grams} \]

Therefore, the 2-liter bottle would have

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

of dissolved solids.