Knowee
Questions
Features
Study Tools

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

Question

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

🧐 Not the exact question you are looking for?Go ask a question

Solution

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 x .
  • The expression for "four less than a number" is x4 x - 4 .
  • The quotient of this expression divided by 5 is x45 \frac{x - 4}{5} .
  • The number divided by 8 is x8 \frac{x}{8} .

2. Relevant Concepts

According to the problem, these two expressions are equal: x45=x8 \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(x4)=5x 8(x - 4) = 5x
  2. Distribute on the left side: 8x32=5x 8x - 32 = 5x
  3. Get all terms involving x x on one side: 8x5x=32 8x - 5x = 32 3x=32 3x = 32
  4. Solve for x x : x=323 x = \frac{32}{3}

4. Verify and Summarize

  • Substituting x=323 x = \frac{32}{3} back into the original expressions: Left Side: x45=32345=3231235=2035=2015=43 \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} Right Side: x8=3238=3224=43 \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 323 \frac{32}{3} or approximately 10.67 10.67 .

This problem has been solved

Similar Questions

The quotient of two numbers is 5. Their difference is 4. What are the two numbers?

The difference of two numbers is 8. Their quotient is 9. What are the two numbers?

Create an expression that shows "eight divided by two raised to the power of four".Then, evaluate the expression.Reset Submit

The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:

Four more than half of certain number is seven less than the number. What is the number?

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.