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# John believes that the amount of sleep he gets the night before a test and his score on that test are inversely related. On his first exam,

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John believes that the amount of sleep he gets the night before a test and his score on that test are inversely related. On his first exam, he got eight hours of sleep and scored 70 on the exam. To the nearest tenth, how many hours does John believe he must sleep the night before his second exam so that the average of his two exam scores is an 80?

Jul 20, 2022

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To average an 80   he must score a 90  on the  second exam

So....in the first case

8 =  k / 70   where k is the proportionality constant

70 * 8 =  k =  560

So....in the second  case

90 =  560 / S     where S is the hours of sleep

S  = 560 / 90  =  56/9   ≈  6.2 hrs of sleep   Jul 20, 2022

#1
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The answer is 90*8/70, which rounds to 10.3.

Jul 20, 2022
#2
+1

To average an 80   he must score a 90  on the  second exam

So....in the first case

8 =  k / 70   where k is the proportionality constant

70 * 8 =  k =  560

So....in the second  case

90 =  560 / S     where S is the hours of sleep

S  = 560 / 90  =  56/9   ≈  6.2 hrs of sleep   CPhill Jul 20, 2022