So I have this problem I can't seem to solve, I might be overthinking it, english is not my first language...
The sample size is 1525,
Total all groups: 45% agree, 45% disagree, 10% didn't answer
Group a) 90% agree 6% disagree 4% didn't answer
Group b) 40% agree 45% disagree 15% didn't answer
Group c) 14% agree 81% disagree 5% didn't answer
How many people were in group a?
Thanks in advance. If the final number is a range (between x&y) please let me know.
Let $a,b,c$ the porportion of the groups. Then you have the following linear equation system.
$$0.9a+0.4b+0.14c=0.45$$
$$0.06a+0.45b+0.81c=0.45$$
$$a+b+c=1$$
The third equation uses the fact that the porportions have to add up to 1.
The solution is $(a,b,c)=(0.229008,0.522901,0.248092)$
The number of people in group a is $0.229008\cdot 1525\approx 349.24$. We have to round off. Thus $a^*=349$
There must be a mistake in the exercise because $0.45\cdot 1525=668.25$. The number people who agree/disagree should be a whole number as well.
Or the porpotions itself have been already rounded. In this case the solution $a^*$ is OK.