If Francis spends $\frac{1}{3}$ of his day sleeping, $\frac{1}{4}$ of his day studying and $\frac{1}{8}$ of his day eating, how many hours in the day does he have left?
(A) 4
(B) 6
(C) 5
(D) 7
(E) 9
Solution 1

Since there are 24 hours in a day, Francis spends $\frac{1}{3} \times 24=8$ hours sleeping.

Also, he spends $\frac{1}{4} \times 24=6$ hours studying, and $\frac{1}{8} \times 24=3$ hours eating.

The number of hours that he has left is $24-8-6-3=7$ hours.

## Solution 2

Francis spends $\frac{1}{3}+\frac{1}{4}+\frac{1}{8}=\frac{8+6+3}{24}=\frac{17}{24}$ either sleeping, studying or eating.

This leaves him $1-\frac{17}{24}=\frac{7}{24}$ of his day.

Since there are 24 hours in a full day, then he has 7 hours left.

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