It's rational because it contains a repeating digit pattern, 743 (first option).
In particular, if
<em>x</em> = -6.743743…,
then
1000<em>x</em> = -6,743.743743… .
Subtracting, we can eliminate the trailing end and solve for <em>x</em> exactly:
1000<em>x</em> - <em>x</em> = -6,743.743743… - (-6.743743…)
999<em>x</em> = -6,737
<em>x</em> = -6,737/999
N+(n+1) = 85. 2n+1=85, 2n=84. n=42. So the consecutive integers are 42 and 43, and the larger one is 43.
The fraction he added is 6/30, or 1/5.
I'm not 100% sure about the equation you want me to use but I did the work this way:
5/6+x/30=31/30 (the denominator has to equal 30 because you are adding. You need a common denominator which is why you need to change 5/6. We can label the numerator as a hidden value x)
25/30+x=31/30
You can then work backwards and basically subtract 25 from 31 and get 6; so x=6
So there are x girls and x-4 boys and together they make 28:
x+x-4=28
2x-4=28
2x=32
x=16
so there are 16 girls and 12 boys.
the ratio is then 16:12, or we can simplify (by dividing both sides by 4): 4:3
so the best answer is 4:3.
