Math Problem Statement

two less than the quotient of a number and five is one

Solution

The problem states: "two less than the quotient of a number and five is one." Let's break it down and form an equation.

  • Let the unknown number be xx.
  • The "quotient of a number and five" translates to x5\frac{x}{5}.
  • "Two less than the quotient" means subtracting 2 from x5\frac{x}{5}, which gives us x52\frac{x}{5} - 2.
  • This expression equals 1, so the equation is:

x52=1\frac{x}{5} - 2 = 1

Solving the equation:

  1. Add 2 to both sides to get rid of the -2: x5=3\frac{x}{5} = 3

  2. Multiply both sides by 5 to solve for xx: x=15x = 15

Final Answer:

The number is x=15x = 15.

Would you like further explanation, or do you have any questions?

Here are 5 related questions for practice:

  1. Three more than the quotient of a number and four is five.
  2. The sum of a number and eight is equal to twice the number.
  3. Five less than twice a number is equal to three.
  4. The difference between a number and nine is equal to four times the number.
  5. The quotient of a number and three, plus seven, is equal to ten.

Tip: Always break down word problems by identifying key phrases like "less than," "quotient," or "product" to form the correct equation.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Quotients

Formulas

Quotient of a number x divided by a constant: x / constant
Linear equation: ax + b = c

Theorems

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Suitable Grade Level

Grades 6-8