In a random sample of 100 Americans of voting age, 10 more Americans identify themselves as Independents than Republicans. Six fewer Americans identify themselves as Republicans than Democrats. Assuming that all of those sampled are Republican, Democrat, or Indepenent, how many of those in the sample identify themselves with each political affiliation?
I have to put this into a system of equation. Is this the right way to set it up into a system of equations? This is what I came up with.
r = i+10
d = r - 6
d + r + i = 100
2007-03-22 19:28:33 · 3 answers · asked by World Expert 1 in Education & Reference ➔ Homework Help
Close.
r = d - 6
i= r + 10
d + r + i = 100 (that one was right)
To help with the last equation, if you need to solve it, it may help to change that first one to "d = r + 6". This way, you can substitute i and d with their equivalents in the last equation, and solve for r, then use that in the two previous equations to solve for i and d.
(r + 6) + r + (r + 10) = 100
3r + 16 =100
3r = 84
r = 28
i = 28+10 = 38
d = 28 + 6 = 34
2007-03-22 19:31:47 · answer #1 · answered by Master Maverick 6 · 1⤊ 0⤋
Yes, I agree with the others answers... you got the middle equation a little wrong. Since there are six fewer Americans that identify themselves as Republicans than Democrats, that means (inversely) that there are six more Americans that identify themselves as Democrats than as Republicans, so:
r + 6 = d
The other two equations are correct... good job!
2007-03-22 19:47:19 · answer #2 · answered by Erik M 2 · 0⤊ 0⤋
10 more independents than republicans, i=r+10
6 less republicans than democrats, r=d-6
you have the final equation correct.
2007-03-22 19:40:38 · answer #3 · answered by molniya 2 · 0⤊ 0⤋