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Zorluk: OrtaRatios, Rates, and Proportions

A solar-powered charging station operates using two types of solar panels, Type A and Type B. The ratio of Type A panels to Type B panels installed at the station is 5:35 : 3. Each Type A panel generates 2424 watt-hours of energy per hour, and each Type B panel generates 4040 watt-hours of energy per hour. If there are a total of 4848 solar panels installed at the station, how many total watt-hours of energy do all the panels generate combined in one hour?

  1. A
    240240
  2. B
    1,5361,536
  3. 1,4401,440Cevap
  4. D
    1,6321,632
  5. E
    1,9201,920

Cevap

The total energy generated by all panels in one hour is 1,4401,440 watt-hours.
The correct answer is 1,4401,440 watt-hours. The ratio 5:35 : 3 indicates that out of every 8 panels (5+35 + 3), 5 are Type A and 3 are Type B. Converting these to fractions of the total 4848 panels gives 48×58=3048 \times \frac{5}{8} = 30 Type A panels and 48×38=1848 \times \frac{3}{8} = 18 Type B panels. Multiplying each quantity by its respective hourly output yields 30×24=72030 \times 24 = 720 watt-hours for Type A panels and 18×40=72018 \times 40 = 720 watt-hours for Type B panels. Combining these gives 720+720=1,440720 + 720 = 1,440 watt-hours.

Adım Adım Çözüm

1
Calculate the total number of ratio parts
The total ratio parts equal 5+3=85 + 3 = 8.
To divide the total number of panels into proportional parts, add the terms of the ratio together.
2
Find the quantity of each type of panel installed
Type A panels = 48×58=3048 \times \frac{5}{8} = 30; Type B panels = 48×38=1848 \times \frac{3}{8} = 18.
Multiply the total number of panels (4848) by each panel type's fraction of the total ratio.
3
Calculate the energy generated by each panel type in one hour
Type A energy = 30×24=72030 \times 24 = 720 watt-hours; Type B energy = 18×40=72018 \times 40 = 720 watt-hours.
Multiply the count of each panel type by its specific hourly generation rate.
4
Sum the energy outputs to find the combined total
Total combined energy = 720+720=1,440720 + 720 = 1,440 watt-hours.
Add the hourly energy outputs of Type A and Type B panels together.

Anahtar Kavram

Solving multi-step word problems involving part-to-whole ratios and rate calculations
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Ratios, Rates, and Proportions

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