A landscaper is managing water in a large reservoir tank for a greenhouse. The tank initia… — Armed Services Vocational Aptitude Battery (ASVAB)

A landscaper is managing water in a large reservoir tank for a greenhouse. The tank initially contains $10 \frac{1}{4}$ gallons of water. The landscaper adds $3 \frac{1}{2}$ gallons of water from a reserve hose. Over the hot afternoon, $1 \frac{7}{8}$ gallons of water evaporate from the open tank. Finally, the landscaper drains $4 \frac{2}{3}$ gallons to water a specific batch of plants. Calculate the final volume of water remaining in the tank.

Answer:After all changes, there are exactly 【7 5/24】 gallons of water remaining in the tank. (Enter your answer as a simplified mixed number, e.g., '2 1/2' or '5 3/4')

Answer

7 5/24

The correct answer is found by establishing a common denominator of 24 for all fractional parts, summing the additions, subtracting the removals, and properly regrouping the whole numbers when subtracting a larger fraction from a smaller one.

Step-by-Step Solution

Find a common denominator for all the fractions involved:

1/4

1/2

7/8

, and

2/3

The least common multiple of 4, 2, 8, and 3 is 24.

Fractions must have the same denominator to be added or subtracted.

Convert all mixed numbers to equivalent fractions with a denominator of 24 and calculate the total amount after adding water.

10 \frac{6}{24} + 3 \frac{12}{24} = 13 \frac{18}{24}

gallons.

This establishes the total volume of water in the tank before any is removed or lost.

Subtract the evaporated volume (

1 \frac{7}{8}

) from the total.

Convert

1 \frac{7}{8}

1 \frac{21}{24}

. Subtract:

13 \frac{18}{24} - 1 \frac{21}{24}

. Because 18 is less than 21, regroup 1 whole from 13:

12 \frac{42}{24} - 1 \frac{21}{24} = 11 \frac{21}{24}

gallons.

Evaporation reduces the total volume, and regrouping is necessary to subtract a larger fractional part from a smaller one.

Subtract the drained volume (

4 \frac{2}{3}

) from the remaining amount.

Convert

4 \frac{2}{3}

4 \frac{16}{24}

. Subtract:

11 \frac{21}{24} - 4 \frac{16}{24} = 7 \frac{5}{24}

gallons.

This accounts for the final removal of water to find the true end volume.

Key Concept

Adding and subtracting mixed numbers with unlike denominators, requiring regrouping.

Estimated Time:3m 0s

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