is my solution right? the 0 in the ratio seems strange
The red lamp brigade patrols the 3600 sectors of the galaxy along with their better known counterparts the Green lantern corps. Each sector has either one corps member or one brigadier. In the first 2400 sectors, the ratio of corps members to brigadiers is 3:1. If there are an equal number of brigadiers and crops members in the galaxy, what is the ratio of corps members to brigadiers in the other sectors?
c=b
c+b=3600
c=b=1800
in the first 2400 sectors there are 3corps:1brigadier
2400/4=600 groups of 3corps+1brigadier
3*600=1800 corps
1*600=600 brigadier
the number of corps is equal to c so there wont be any other corps
we have 1800-600=1200 brigadier left
3600-2400=1200 sector left
the ratio is 0 corp:1200 brigadier
you went the long way around, but got the right answer.
3:1 = 1800:600
That leaves 1200 sectors
600+1200 = 1800
so, 1200 brigadiers and 0 corp
yeah sorry i'm kinda slow. thank you
Im kinda confused, what is the ratio of corps members to brigadiers in the other sectors?
Is it 0:1200?
Yep
0:1200 is what I got too!
Is this from the AoPs Introduction to Algebra book? That's where I found it. I got 0:1200 as well!!!
0:1200 is what i got too
but still confused why is it 0 corps????
To check if your solution is correct, let's analyze the problem step by step.
First, you correctly defined the variables:
- c represents the number of corps members (corps)
- b represents the number of brigadiers (brigadier)
Next, you correctly determined the total number of sectors:
c + b = 3600
Since it is mentioned that there are an equal number of brigadiers and corps members in the galaxy, we can conclude that c = b.
Substituting c = b into the equation:
b + b = 3600
2b = 3600
b = 1800
Now, for the first 2400 sectors, the ratio of corps members to brigadiers is given as 3:1.
To find the number of corps members in the first 2400 sectors, you divided 2400 by 4 (3 corps + 1 brigadier) to obtain the number of groups. Then you multiplied the number of groups (600) by the number of corps members in each group (3), resulting in 1800 corps members in the first 2400 sectors. Similarly, you found that there are 600 brigadiers in the first 2400 sectors.
Now, we need to determine the ratio for the remaining sectors (3600 sectors - 2400 sectors = 1200 sectors) where there are only brigadiers.
Since the number of corps members is equal to c (1800) and we know that there are no more corps members, the ratio for the remaining sectors will be 0 corps members to the remaining brigadiers.
So the correct ratio is indeed 0 corps members : 1200 brigadiers for the remaining sectors.
Therefore, your solution is correct.