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Zorluk: Çok zorCalculating Percentages of Quantities

Read the scenario carefully and calculate the final amount of fuel. Enter the exact numerical value in the blank.

Cevap:A military logistics base begins a major operation with 12,00012,000 gallons of fuel in reserve. During the first phase of the operation, 35%35\% of the initial fuel supply is consumed. During the second phase, 45%45\% of the *remaining* fuel is consumed. Following the second phase, a resupply convoy delivers an amount of fuel equal to 25%25\% of the fuel that was consumed during the first phase. After the delivery, there are 【5340】 gallons of fuel in the reserve.

Cevap

5340
The correct answer accurately tracks the changing base values for each percentage calculation. First, find 35%35\% of the initial 12,00012,000 gallons (4,2004,200 used), leaving 7,8007,800 gallons. Next, find 45%45\% of the remaining 7,8007,800 gallons (3,5103,510 used), leaving 4,2904,290 gallons. Finally, calculate a resupply of 25%25\% of the first phase's consumption (25%25\% of 4,200=1,0504,200 = 1,050). Adding this resupply gives 4,290+1,050=5,3404,290 + 1,050 = 5,340 gallons.

Adım Adım Çözüm

1
Calculate the fuel consumed in the first phase by multiplying the initial amount (12,00012,000 gallons) by 35%35\%.
0.35×12,000=4,2000.35 \times 12,000 = 4,200 gallons.
This determines the amount of fuel used during the initial stage based on the total starting quantity.
2
Subtract the consumed fuel from the initial amount.
12,000−4,200=7,80012,000 - 4,200 = 7,800 gallons.
The second phase's percentage is based on the remaining fuel, not the original total.
3
Calculate the fuel consumed in the second phase by multiplying the remaining fuel (7,8007,800 gallons) by $45\%.
0.45×7,800=3,5100.45 \times 7,800 = 3,510 gallons.
This finds the fuel used in the second stage based on the updated base value.
4
Subtract the second phase consumption from the fuel available before the second phase.
7,800−3,510=4,2907,800 - 3,510 = 4,290 gallons.
This determines the total remaining fuel before the resupply.
5
Calculate the resupply amount by multiplying the fuel consumed in the first phase (4,2004,200 gallons) by $25\%.
0.25×4,200=1,0500.25 \times 4,200 = 1,050 gallons.
The resupply is specifically defined as a percentage of a previously calculated quantity (Phase 1 consumption), not the remaining fuel.
6
Add the resupply amount to the fuel remaining after the second phase.
4,290+1,050=5,3404,290 + 1,050 = 5,340 gallons.
This gives the final total of fuel in the reserve.

Anahtar Kavram

Calculating percentages of varying base quantities in multi-step word problems.
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Konular

Calculating Percentages of Quantities

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