Question 351·Hard·Math

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The stacked bar chart shows the total electricity generated in a country in 2010 and 2020, along with the amount generated from renewable sources.

If $q\%$ is the percent of the net increase in total electricity from 2010 to 2020 that is accounted for by the increase in renewable electricity, what is the value of $q$ ?

In a stacked bar chart, the top of each bar gives the total, while a segment shows one part. For a percent of a net increase, find the change in the total and the change in the named part, then compare those two changes. Don't divide by the earlier year's total. The part's increase can exceed the net increase if another part decreases.

Hints

Hint 1
In a stacked bar chart, the top edge gives the total; it isn't a second amount to add to the bottom segment. Which heights show the complete bars, and which show renewable electricity?
Hint 2
A net increase is the change in the whole amount after its parts' changes combine. Subtract the earlier total from the later total, then make a separate subtraction for renewable electricity.
Hint 3
In a part-to-whole percent, the base is the amount treated as $100\%$ . Here you're comparing one increase with another, not with an amount from 2010. Which increase is $q\%$ taken of?

Step-by-step

Compare the two increases
Step 1
Read the segment and total heights
The light segments start at zero, so renewable electricity is $40$ TWh in 2010 and $90$ TWh in 2020. The complete bars reach $160$ and $180$ TWh. The top of each bar is already the total, so don't add the renewable height to it.
Step 2
Find the net increase in total electricity
Type $180-160$ into Desmos. It shows $20$ , so the total electricity increased by $20$ TWh.
Step 3
Find the increase in renewable electricity
Type $90-40$ on the next Desmos line. It shows $50$ , so renewable electricity increased by $50$ TWh.
Step 4
Make the net increase the percent base
In a part-to-whole percent, the base is what the percent is taken of. The question asks how much of the $20$ TWh net increase is accounted for by the $50$ TWh renewable increase, so write: $q\%\text{ of }20=50$ . Compare the increase in the part with the net increase in the whole. Using either year's total as the base would answer a different question.
Step 5
Solve for the percent
Type $q_{1}\%\operatorname{of}20\sim50$ in Desmos. Here $q_1$ stands for $q$ , and $\sim$ tells Desmos to find the value that makes both sides match. Under PARAMETERS, it shows $q_1=250$ . So renewable growth accounts for $250\%$ of the net increase. That's more than $100\%$ because nonrenewable electricity decreased, offsetting some renewable growth. Choice C.

Question 351·Hard·Math

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