A residential solar power system generated 4{}000 kilowatt-hours (\text{kWh}) of electrici… — GRE General Test

A residential solar power system generated $4{}000$ kilowatt-hours ( $\text{kWh}$ ) of electricity during its first year of operation. In the second year, electricity generation decreased by $10\%$ . In the third year, electricity generation increased by $10\%$ relative to the second year's generation. How many kilowatt-hours of electricity did the solar system generate in the third year?

A
$3{}240$
B
$3{}600$
$3{}960$ Cevap
D
$4{}000$
E
$4{}400$

Cevap

The solar power system generated

3{}960\text{ kWh}

of electricity in the third year.

In the first year, generation was

4{}000\text{ kWh}

. A

10\%

decrease yields

4{}000 \times (1 - 0.10) = 3{}600\text{ kWh}

for the second year. In the third year, a

10\%

increase over the second year's generation yields

3{}600 \times (1 + 0.10) = 3{}960\text{ kWh}

Adım Adım Çözüm

Calculate the electricity generated in the second year after a

10\%

decrease from the first year.

4{}000 - (0.10 \times 4{}000) = 4{}000 - 400 = 3{}600\text{ kWh}

10\%

decrease means retaining

90\%

of the original

4{}000\text{ kWh}

base.

Calculate the electricity generated in the third year after a

10\%

increase over the second year's total.

3{}600 + (0.10 \times 3{}600) = 3{}600 + 360 = 3{}960\text{ kWh}

The

10\%

increase applies to the new base value of

3{}600\text{ kWh}

, not the initial

4{}000\text{ kWh}

Anahtar Kavram

Successive Percent Changes and Base Shifts

Tahmini Süre:45s

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

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