A supply truck initially carries 78 \frac{3}{4} tons of cargo. The driver unloads \frac{1}… — Armed Services Vocational Aptitude Battery (ASVAB)

A supply truck initially carries $78 \frac{3}{4}$ tons of cargo. The driver unloads $\frac{1}{3}$ of the total cargo at the first outpost. At the second outpost, the driver unloads $\frac{3}{5}$ of the *remaining* cargo.

How many tons of cargo are left on the truck after both deliveries are made?

Cevap:Remaining cargo: 【21】 tons

Cevap

21 tons

To find the final amount efficiently, multiply the original total by the fractions representing what remains on the truck after each stop. After dropping off

\frac{1}{3}

, exactly

\frac{2}{3}

of the load remains. After dropping off

\frac{3}{5}

of that remainder, exactly

\frac{2}{5}

of it remains. We calculate the final remaining amount as:

78 \frac{3}{4} \times \frac{2}{3} \times \frac{2}{5}

. Converting to an improper fraction, this becomes

\frac{315}{4} \times \frac{2}{3} \times \frac{2}{5}

. Multiplying the two remaining fractions first gives

\frac{4}{15}

. Finally,

\frac{315}{4} \times \frac{4}{15} = \frac{315}{15} = 21

tons.

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Calculate the amount of cargo left after the first delivery.

52 \frac{1}{2}

tons remain.

Since

\frac{1}{3}

of the cargo is unloaded,

1 - \frac{1}{3} = \frac{2}{3}

of the original cargo remains. Multiplying the original amount

\frac{315}{4}

\frac{2}{3}

yields

\frac{105}{2}

52 \frac{1}{2}

tons.

Calculate the amount of cargo left after the second delivery.

21 tons remain.

The driver unloads

\frac{3}{5}

of the remaining cargo, meaning

1 - \frac{3}{5} = \frac{2}{5}

of it is still on the truck. Multiplying the remaining

\frac{105}{2}

tons by

\frac{2}{5}

gives exactly 21 tons.

Anahtar Kavram

Calculating successive fractional parts by determining the remainder at each step.

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