I28-07

Question

A solar energy project involves installing solar panels over a total area of 240 square meters and has two design strategies to choose from. Strategy 1 uses the entire 240 square meters for a single high-efficiency solar panel setup, which provides an electrical output equal to 0.5kWH per square meter. Strategy 2 splits the area into two separate setups: 200 square meters with a slightly lower efficiency that provides an electrical output equal to 0.4kWH per square meter and the remaining 40 square meters with an output of  x  kWH per square meter. Both strategies are otherwise identical, and all electrical output is calculated at the end of the year.
 
Select for  x  the value of  x  at which the two strategies result in the same total electrical output, and select for  y  the value at which the output from the 200 square meters setup would be exactly twice the additional output from the 40 square meters setup. Make only two selections, one in each column.

Bunuel · Answer

Official Solution:

Let’s first calculate the total electrical output for both strategies and solve for the given conditions.
 
 Strategy 1 
 
The total output from Strategy 1 using the entire 240 square meters at 0.5 kWH per square meter:
 
 240 * 0.5 = 120  kWH
 
 Strategy 2 
 
1. The output from the 200 square meters at 0.4 kWH per square meter:
 
 200 * 0.4 = 80  kWH
 
2. The output from the remaining 40 square meters at  x  kWH per square meter:
 
 40x  kWH
 
The total output from Strategy 2 is:
 
 80 + 40x  kWH
 
 Solving for  x  in the First Column 
 
To make the total output of both strategies equal:
 
 120 = 80 + 40x 
 
 40 = 40x 
 
 x = 1.0 
 
 Solving for  y  in the Second Column 
 
We want the output from the 200 square meters setup (80 kWH) to be twice the output from the 40 square meters setup at  y  kWH per square meter:
 
 80 = 2 * (40y) 
 
 80 = 80y 
 
 y = 1.0

Correct answer:

x  "1"

y  "1"

Charlotte825 · Answer

I like the solution - it’s helpful. I understood that y was referring to the output of the 200 square meter field, and x=1 is set, so I felt like 0.4 should have been the answer. I agree with the solution, I just believe that it would be helpful to state, that y also refers to the 40 square meters output and not 200.

Otherwise very nice and engaging question.

Bunuel · Answer

y refers to the 40 m^2 setup, not the 200 m^2.

x = 1 comes from the first part only. The second part is a separate condition where y is a new variable for the 40 m^2 setup.

Jay29 · Answer

The word additional is confusing. The statement makes me question if I have to find the value for y when, we consider the output from 40 meter square to be 0.4 KWH and then consider the additional KWH output required to satisfy the condition.

Bunuel · Answer

Here, “additional output” means the output from the additional 40 square meters setup, not the extra output above 0.4 kWH.

I28-07

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