Tired Interns

nik08 wrote:At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent of the interns report no feelings of tiredness during their shifts?

A. 6
B. 14
C. 19
D. 20
E. 81

Can someone help?

parallel_chase wrote:

nik08 wrote:At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent of the interns report no feelings of tiredness during their shifts?

A. 6
B. 14
C. 19
D. 20
E. 81

Can someone help?

Lets there be 100 interns.

75 sleep less than 6 hours
25 sleep more than 6 hours

70% of 25 = interns sleep more than 6 hours and report no feeling of tiredness

70/100 * 25 = 17.5

if 80 people sleep less then 6 hours then.

17.5/75 = x/80

17.5 * 80 = 75*x

x=18.6

the answer should be 19.

Hope this helps.