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Zorluk: OrtaFractions, Decimals, and Percents Arithmetic

A cargo logistics warehouse handles three types of freight: Standard, Express, and Fragile. At the start of the week, 25\frac{2}{5} of the total shipments in the warehouse were Standard freight, 0.350.35 of the total shipments were Express freight, and the remaining shipments were Fragile freight. During a midweek inventory adjustment, the number of Standard freight shipments increased by 25%25\%, the number of Express freight shipments decreased by 20%20\%, and the number of Fragile freight shipments remained unchanged at 125125 units. What was the total number of shipments in the warehouse after the midweek inventory adjustment?

Cevap: 515 shipments

Cevap

515 shipments
Converting 25\frac{2}{5} to a decimal gives 0.400.40. The initial proportion of Fragile freight is 1−0.40−0.35=0.251 - 0.40 - 0.35 = 0.25. Since Fragile freight equals 125125 shipments, the initial total number of shipments is 1250.25=500\frac{125}{0.25} = 500. Prior to adjustment, the warehouse has 0.40×500=2000.40 \times 500 = 200 Standard shipments and 0.35×500=1750.35 \times 500 = 175 Express shipments. After the adjustment, Standard shipments increase to 200×1.25=250200 \times 1.25 = 250, Express shipments decrease to 175×0.80=140175 \times 0.80 = 140, and Fragile shipments remain 125125. Summing these post-adjustment counts yields 250+140+125=515250 + 140 + 125 = 515 shipments.

Adım Adım Çözüm

1
Determine the initial fraction representing Fragile freight.
Fragile freight constitutes 0.250.25 (or 25%25\%) of the total initial shipments.
Converting 25\frac{2}{5} to a decimal yields 0.400.40. Subtracting the Standard (0.400.40) and Express (0.350.35) proportions from the total (1.001.00) leaves 1.00−0.40−0.35=0.251.00 - 0.40 - 0.35 = 0.25.
2
Calculate the total initial number of shipments in the warehouse.
Initial total shipments = 500500.
Since 25%25\% of the total initial shipments equals 125125 Fragile units, the initial total is 1250.25=500\frac{125}{0.25} = 500.
3
Calculate the initial quantities of Standard and Express shipments.
Initial Standard shipments = 200200, Initial Express shipments = 175175.
Standard shipments = 0.40×500=2000.40 \times 500 = 200, and Express shipments = 0.35×500=1750.35 \times 500 = 175.
4
Apply the inventory percentage changes to each category.
New Standard shipments = 250250, New Express shipments = 140140, Fragile shipments = 125125.
A 25%25\% increase in Standard shipments gives 200×1.25=250200 \times 1.25 = 250. A 20%20\% decrease in Express shipments gives 175×0.80=140175 \times 0.80 = 140. Fragile shipments remain 125125.
5
Sum the adjusted shipment counts to determine the net total.
Final total shipments = 515515.
Adding the three updated categories gives 250+140+125=515250 + 140 + 125 = 515.

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Fractions, Decimals, and Percents Arithmetic
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