A marine biology research team collected a water sample from an estuary to analyze its com… — ACT

A marine biology research team collected a water sample from an estuary to analyze its composition. In the sample, $\frac{3}{10}$ of the total volume is saltwater, $45\%$ of the total volume is brackish water, and $0.05$ of the total volume is mineral sediment. The remaining portion of the sample is freshwater. What fraction of the total sample volume is freshwater?

A
$\frac{1}{10}$
B
$\frac{1}{4}$
$\frac{1}{5}$ Answer
D
$\frac{7}{20}$
E
$\frac{2}{5}$

Answer

The fraction of the total sample volume that is freshwater is

\frac{1}{5}

Converting all three non-freshwater portions to decimals yields

0.30

(saltwater),

0.45

(brackish water), and

0.05

(sediment). Adding these together gives

0.80

. Subtracting

0.80

from the total sample volume of

1.00

leaves

0.20

, which converts to the simplified fraction

\frac{1}{5}

Step-by-Step Solution

Convert all given volume proportions into decimals.

Saltwater =

\frac{3}{10} = 0.30

, Brackish water =

45\% = 0.45

, Mineral sediment =

0.05

Converting all components to a common decimal format allows direct addition.

Sum the proportions of saltwater, brackish water, and mineral sediment.

0.30 + 0.45 + 0.05 = 0.80

This calculates the combined proportion of the sample that is not freshwater.

Subtract the combined non-freshwater proportion from the whole sample (

1.00

1.00 - 0.80 = 0.20

The remainder of the sample represents the freshwater component.

Convert the decimal portion to a simplified fraction.

0.20 = \frac{20}{100} = \frac{1}{5}

The question asks for the proportion formatted as a simplified fraction.

Key Concept

Converting between fractions, decimals, and percentages to solve multi-step word problems.

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