Problem
Redraw with one item as the new whole
One graph gives the turnout of an election and another splits the votes cast among candidates. We need one candidate's vote count.
RatiosData & probability
Your answer
How to solve
Strategy Change Focus / Count the Complement — The second graph takes one slice of the first and blows it up into a whole bar. So the chain runs in one direction only: eligible voters, then votes cast, then one candidate's share of those.
1STEP 1
Find the turnout
If 20% did not vote, the rest did.
100 - 20 = 80
80% of voters turned out.
6.SP.B.4Analyze The Units2STEP 2
Count the votes cast
Take that share of the five million eligible voters.
5000000 × 0.8 = 4000000
4 million votes were cast.
6.RP.A.3Organize Information In More Ways3STEP 3
Find candidate A's share
The vote-share bar covers only the votes cast, and its five sections add to 100%.
100 - 35 - 11 - 5 - 4 = 45
A took 45% of the votes cast.
6.SP.B.4Change Focus Count The ComplementThe vote-share bar's is the votes cast, not the voters.
Why?
The bar's five sections are the candidates' shares of the ballots that were actually put in, and every such ballot is in exactly one section.
🧱One-to-one correspondenceIf each thing here pairs with exactly one thing there, the two groups are the same size.
Why?
Those sections leave nothing out and overlap nowhere, so together they are the whole of the votes cast and nothing more.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
4STEP 4
Apply it to the votes cast
Take 45% of the four million votes -- not of the five million voters.
4000000 × 0.45 = 1800000
A received 1,800,000 votes.
6.RP.A.3Organize Information In More WaysAnswer
1,800,000 votes
Add the five candidates' votes: 1,800,000 + 1,400,000 + 440,000 + 200,000 + 160,000 comes to 4 million, the votes cast.
Takeaway
When one graph zooms in on a slice of another, its 100% is only that slice.
- Find the turnout
- Count the votes cast
- Find candidate A's share
- Apply it to the votes cast