Kevin E. answered • 06/18/22
Teaching through Understanding
First look at the groups they are talking about. Here, there are three groups, Democrats, Democrats who are Independents, and Republicans.
Next figure out what numbers are present based on the words used. It says that "one-fifth of the Democrats are Independents"; this means that no matter how many democrats you find, 1/5 of them are independent (one-fifth=1/5). This means that D/5=I. It also specifies that "twice as many Republicans as Democrats". This means no matter what the specific number of Democrats is being seen, double it to get to the number of Republicans (2*D=R). It also specifies that the total group size is 304. This means if you add together the Democrats, Republicans, and the Independents together, it will end up being 304. The mathy way of representing this is D+R+I=304.
Since we know that 2*D=R, so in the equation D+R+I=304, we can replace the R term with a 2*D term, giving us D+2*D+I=304 (since we know R=2*D). If one thing equals another thing, we can replace the first thing with the second thing in any equation, because the result will always be identical between the two since those two terms are the same. This means that D+R+I=304 and D+2*D+I=304 will always give the same results since R=2*D.
We can do the same thing with D/5=I. In the equation D+2*D+I=304, we can replace the I term with the D/5 term, since those two terms are equal to each other. So now we have D+2*D+D/5=304. Now combine like terms and solve for D. That will be the number of Democrats.
Now that you know the number of Democrats, you can plug that number in for D in the equation D/5=I to get the number of Independents. You can also plug the number for Democrats in for D in 2*D=R to get the number of Republicans.
If you want me to elaborate on anything, please let me know.
