Write an equation that represents the problem, then solve the problem.

The quotient of a number and 4 is 6. Find the number.
i have to show my work

Question

Write an equation that represents the problem, then solve the problem.

The quotient of a number and 4 is 6.  Find the number.    
i have to show my work

mathstudent55 · Answer

What does quotient mean?

anonymous · Answer

i dont konow

mathstudent55 · Answer

The quotient is the result of a division.
For example, in the division
$$24 \div 4 = 6$$
$6$ is the quotient.

anonymous · Answer

ok

mathstudent55 · Answer

Let "a number" be represented by x since "a number" is an unknown amount.
The quotient of "a number" and 4 is 6 means x divided by 4 equals 6:

$ \dfrac{x}{4} = 6$

Now you need to solve for x.

anonymous · Answer

6 * 4

mathstudent55 · Answer

Correct.
We already have the equation. Now we need to solve it.
We want x by itself because we want to know what x is equal to.
Since x is being divided by 4, to get x by itself, you need to do the opposite of dividing by 4. The opposite of dividing by 4 is multiplying by 4.

mathstudent55 · Answer

In an equation, the rule is that you must do the same thing to both sides of the equation.
Since we need to multuiply the left side by 4 to get x by itself, we also multiply the right side by 4.

$ \dfrac{x}{4} \times 4 = 6 \times 4 $

The x's on the left side cancel out, and we multiply the right side giving the answer:

$x = 24$

anonymous · Answer

ok

mathstudent55 · Answer

The final answer is:
The number is 24.

Notice that the problem was not an equation. The problem was a word problem with a simpe question: Find the number. We used algebra to solve the problem, and we used the variable x, but the person asking the question has nothing to do with x. The answer to "Find the number" is "The number is 24." The answer is not "x = 24."