SOLUTION: A typical college student spends 1/3 of her waking time in class, 1/5 of her waking time eating, 1/10 of her waking time working out, 3 hours studying, and 2.5 hours doing other th

Question 153278: A typical college student spends 1/3 of her waking time in class, 1/5 of her waking time eating, 1/10 of her waking time working out, 3 hours studying, and 2.5 hours doing other things. How many hours of sleep does the typical college student get?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A typical college student spends 1/3 of her waking time in class, 1/5 of her waking time eating, 1/10 of her waking time working out, 3 hours studying, and 2.5 hours doing other things. How many hours of sleep does the typical college student get?
:
Let x = no. of hrs of sleep
then
(24-x) = waking time
:
class + eating + working out + studying + other things + sleeping = 24
(24-x) + (24-x) + (24-x) + 3 + 2.5 + x = 24
:
Multiply equation by 30 to get rid of the denominators; results:
10(24-x) + 6(24-x) + 3(24-x) + 30(3) + 30(2.5) + 30x = 30(24)
:
Get rid of the brackets
240 - 10x + 144 - 6x + 72 - 3x + 90 + 75 + 30x = 720
Group like terms
-10x - 6x - 3x + 30x + 240 + 144 + 72 + 90 + 75 = 720
:
11x + 621 = 720
:
11x = 720 - 621
:
11x = 99
x =
x = 9 hrs spent sleeping
:
:
Check solution in original equation: (Waking = 24 - 9 = 15 hrs)
(15) + (15) + (15) + 3 + 2.5 + x = 24
;
5 + 3 + 1.5 + 3 + 2.5 + 9 = 24; confirms our solution
:
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