The quotient of four less than a number and five is the same as the number divided by eight.

Let's solve the problem step-by-step.

1. Break Down the Problem

We need to set up an equation based on the information given:

• Let the unknown number be $x$.
• The expression for "four less than a number" is $x - 4$.
• The quotient of this expression divided by 5 is $\frac{x - 4}{5}$.
• The number divided by 8 is $\frac{x}{8}$.

2. Relevant Concepts

According to the problem, these two expressions are equal: $\frac{x - 4}{5} = \frac{x}{8}$

3. Analysis and Detail

Now, let's solve the equation.

1. Cross multiply to eliminate the fractions: $8(x - 4) = 5x$
2. Distribute on the left side: $8x - 32 = 5x$
3. Get all terms involving $x$ on one side: $8x - 5x = 32$ $3x = 32$
4. Solve for $x$: $x = \frac{32}{3}$

4. Verify and Summarize

• Substituting $x = \frac{32}{3}$ back into the original expressions: $\text{Left Side: } \frac{x - 4}{5} = \frac{\frac{32}{3} - 4}{5} = \frac{\frac{32}{3} - \frac{12}{3}}{5} = \frac{\frac{20}{3}}{5} = \frac{20}{15} = \frac{4}{3}$ $\text{Right Side: } \frac{x}{8} = \frac{\frac{32}{3}}{8} = \frac{32}{24} = \frac{4}{3}$ Both sides are equal, confirming our solution is correct.

Final Answer

The number is $\frac{32}{3}$ or approximately $10.67$.