Question

jasmine sleeps for an average of 6 hours each day. If Jasmine sleeps for 1/3 the amount of time that her cat sleeps each day, which of the following equations can be used to find x, the number of hours Jasmine's cat sleeps each day?
A. 6x = 1/3
B. 3x = 6
C. x - 1/3 = 6
D. x/3 = 6

Answer 1

To solve the problem, we want to find how many hours Jasmine's cat sleeps each day, which we'll denote as \( x \).

According to the problem, Jasmine sleeps for 1/3 the amount of time that her cat sleeps. This can be expressed with the equation:

\[
\frac{1}{3}x = 6
\]

To find the equivalent equation, we can multiply both sides by 3 to eliminate the fraction:

\[
x = 6 \times 3
\]
\[
x = 18
\]

So, we find that Jasmine's cat sleeps for 18 hours each day.

Now, we can transform the original equation \(\frac{1}{3}x = 6\) to match one of the answer choices. Multiplying both sides by 3 gives:

\[
x = 18
\]

In terms of the options provided:

A. \(6x = \frac{1}{3}\) - This is not correct.
B. \(3x = 6\) - This is also not the original equation we derived.
C. \(x - \frac{1}{3} = 6\) - Not relevant to the problem.
D. \(\frac{x}{3} = 6\) - This can be manipulated to show that \(x = 18\).

Thus, the correct equation that matches our needs and can be used to find \( x \) is:

**D. \( \frac{x}{3} = 6 \)**