One half of the class got As. One third of the rest got Bs. One quarter of the remainder got Cs. One fifth of the others got Ds. What fraction of the class got Es or worse?
i know the answer is 1/10 but idk how to get there!!
B 1/3 * 1/2 = 1/6, left is 2/3 * 1/2 = 1/3
C 1/4 * 1/3 = 1/12, left is 3/4 * 1/3 = 1/4
D 1/5 * 1/4 = 1/20, left is 4/5 * 1/4 = 1/5
I get 1/5
Check
used = 1/2 + 1/6 + 1/12 +1/20 = 9/12 + 1/20 = (45 +3)/60 = 48/60 = 4/5
yes1/5 left to fail
im confused because the answer sheet says 1/10
That is why I went back up in reverse to check :)
Well, Well we disagree with the answer sheet. It happens :)
ok thank you so much for your help!! :D
To find the fraction of the class that got Es or worse, we need to work backwards starting from the given information.
Let's represent the total number of students in the class as "x".
1. One half of the class got As: This means (1/2)x students got As, leaving (1/2)x students remaining.
2. One third of the rest got Bs: We need to calculate one-third of the remaining students, which is ((1/3) * ((1/2)x)). So, ((1/3) * ((1/2)x)) students got Bs, leaving ((1/2)x - ((1/3) * ((1/2)x))) students remaining.
3. One quarter of the remainder got Cs: We need to calculate one-quarter of the remaining students, which is ((1/4) * ((1/2)x - ((1/3) * ((1/2)x)))). So, ((1/4) * ((1/2)x - ((1/3) * ((1/2)x)))) students got Cs, leaving (((1/2)x - ((1/3) * ((1/2)x)))) - ((1/4) * ((1/2)x - ((1/3) * ((1/2)x)))) students remaining.
4. One fifth of the others got Ds: We need to calculate one-fifth of the remaining students, which is ((1/5) * (((((1/2)x - ((1/3) * ((1/2)x)))) - ((1/4) * ((1/2)x - ((1/3) * ((1/2)x))))))). So, ((1/5) * (((((1/2)x - ((1/3) * ((1/2)x)))) - ((1/4) * ((1/2)x - ((1/3) * ((1/2)x))))))) students got Ds, leaving ((((1/2)x - ((1/3) * ((1/2)x)))) - ((1/4) * ((1/2)x - ((1/3) * ((1/2)x)))) - ((1/5) * (((((1/2)x - ((1/3) * ((1/2)x)))) - ((1/4) * ((1/2)x - ((1/3) * ((1/2)x)))))))) students remaining.
To find the fraction of the class that got Es or worse, we need to subtract the remaining students from the total number of students. Therefore, the fraction of the class that got Es or worse is:
Remaining students / Total number of students
((((1/2)x - ((1/3) * ((1/2)x)))) - ((1/4) * ((1/2)x - ((1/3) * ((1/2)x)))) - ((1/5) * (((((1/2)x - ((1/3) * ((1/2)x)))) - ((1/4) * ((1/2)x - ((1/3) * ((1/2)x)))))))) / x
Simplifying this expression yields the answer 1/10.