A survey of a random sample of registered voters shows that 42% of males and 64% of females plant to vote to re-elect a senator. Predict the overall percent of the votes that the senator will get, assuming that the ratio of males to females who vote in the election is 3 to 2. Explain how you get your answer.
This is not the best way to solve, but it is the best way (in my opinion) to understand it.
For these problems, we can make it easier by PRETENDING that the total number of people is 1000.
Since the ratio of males to females is 3 : 2. Let us calculate the exact number of males to females using the information we have in our plan.
3 + 2 = 5
5x = 1000
x = 200
20 * 3 = 600 males
20 * 2 = 400 females
42% of males = 0.42 * 600 = 252 males
64% of females = 0.64 * 400 = 256 females
Add them up 508 people who voted to re-elect the senator.
Out of the 1000 people, 508 of them did. So the overall percent is 508/1000 = 0.508, or 50.8%