A hybrid microgrid power station generates electricity using Solar Array S and Wind Turbin… — GMAT

A hybrid microgrid power station generates electricity using Solar Array S and Wind Turbine W. In Month 1, the ratio of the energy output produced by Solar Array S to that produced by Wind Turbine W was $4 : 3$ .

In Month 2, the energy output of Solar Array S increased by $30\%$ relative to Month 1, while the energy output of Wind Turbine W increased by $10\%$ relative to Month 1. The total energy output produced by both sources combined in Month 2 was $1,700\text{ MWh}$ .

Based on the information provided, which of the following options correctly pairs the energy output of Solar Array S in Month 1 (Column 1) with the energy output of Wind Turbine W in Month 2 (Column 2)?

Column 1: 800 MWh; Column 2: 660 MWhAnswer
B
Column 1: 660 MWh; Column 2: 800 MWh
C
Column 1: 800 MWh; Column 2: 600 MWh
D
Column 1: 1,040 MWh; Column 2: 660 MWh
E
Column 1: 600 MWh; Column 2: 1,040 MWh

Answer

Column 1: 800 MWh; Column 2: 660 MWh

The option specifying Column 1 as 800 MWh and Column 2 as 660 MWh correctly identifies the Month 1 Solar Array S output (

4 \times 200 = 800\text{ MWh}

) and the Month 2 Wind Turbine W output (

3.3 \times 200 = 660\text{ MWh}

Step-by-Step Solution

Define variables based on Month 1 ratio

Let Month 1 output for Solar Array S be

S_1 = 4x

and for Wind Turbine W be

W_1 = 3x

The given ratio of Solar output to Wind output in Month 1 is

4 : 3

Express Month 2 outputs in terms of

x

S_2 = 4x \times (1 + 0.30) = 5.2x

and

W_2 = 3x \times (1 + 0.10) = 3.3x

Solar output increased by

30\%

and Wind output increased by

10\%

in Month 2.

Set up and solve the total output equation for Month 2

5.2x + 3.3x = 8.5x = 1,700 \implies x = 200\text{ MWh}

The combined Month 2 output is given as

1,700\text{ MWh}

Calculate the target quantities for Column 1 and Column 2

Column 1 (

S_1

) =

4 \times 200 = 800\text{ MWh}

; Column 2 (

W_2

) =

3.3 \times 200 = 660\text{ MWh}

Column 1 asks for Solar output in Month 1, and Column 2 asks for Wind output in Month 2.

Key Concept

Two-Part Rate and Ratio Analysis with Multi-Stage Percentage Changes

Estimated Time:2m 30s

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