At a logistics distribution hub, a shipment of incoming packages was processed over two sh… — GMAT

At a logistics distribution hub, a shipment of incoming packages was processed over two shifts. During the morning shift, $0.35$ of the total shipment was processed and dispatched. During the evening shift, $\frac{4}{13}$ of the remaining packages were processed. If $450$ packages remained unprocessed at the end of both shifts, what was the total number of packages in the initial shipment?

Cevap: 1000 packages

Cevap

1000 packages

To find the initial shipment size, first express

0.35

as the fraction

\frac{7}{20}

. Subtracting this from

1

leaves

\frac{13}{20}

of the initial total after the morning shift. Next, processing

\frac{4}{13}

of these remaining packages leaves

1 - \frac{4}{13} = \frac{9}{13}

of that remaining amount. Multiplying

\frac{9}{13} \times \frac{13}{20}

shows that

\frac{9}{20}

of the original total remains unprocessed. Finally, setting

\frac{9}{20}

of the total equal to

450

packages yields an initial total of

1000

packages.

Adım Adım Çözüm

Convert decimal portion to fraction and find remaining fraction after morning shift

Remaining fraction after morning shift is

\frac{13}{20}

Since

0.35 = \frac{7}{20}

of the total shipment was processed,

1 - \frac{7}{20} = \frac{13}{20}

of the initial shipment remained.

Determine the remaining fraction of the shipment after the evening shift

Final remaining fraction of the initial shipment is

\frac{9}{20}

The evening shift processed

\frac{4}{13}

of the remaining packages, leaving

1 - \frac{4}{13} = \frac{9}{13}

of the remaining packages. Thus,

\frac{9}{13} \times \frac{13}{20} = \frac{9}{20}

of the initial shipment remained.

Solve for the total initial number of packages

Total initial packages =

1000

Setting

\frac{9}{20} N = 450

gives

N = 450 \times \frac{20}{9} = 1000

Anahtar Kavram

Combining decimal-to-fraction conversions with successive remaining fraction calculations

Soru

Cevap

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