the product of a number and 4 is 5 less than the quotient of a number and 3

Answer 1

Julius, did you mean to say "quotient of that same number and 3"? If so, you would solve it as follows:

The product is 5 less than the quotient, so add five to the product and set it equal to the quotient:

4x + 5 = x / 3

Multiply both sides by 3: 12x +15 = x

11x = -15

x = -15/11

It checks out:

(-15/11)(4) + 5 = (-15/11) / 3

-60/11 + 55/11 = -15/33

-5/11 = -5/11

Answer 2

This problem is solvable, assuming your variable represents the same unknown value. If that is so, then your equation would be:

4x = x/3 -5

The reason for this is that the product of the unknown and four is five less than the the quotient of the unknown number and 3. Since the product of x and 4 is 5 less than the quotient of x and 3 you have to subtract 5 from the quotient of x and 3.

So, the solution would look like this:

4x = x/3 -5

3(4x) = 3(x/3-5)

12x = x - 15

12x - x = x -x -15

11x = -15

11x/11 = -15/11

x = - 15/11

To check this it is easier to convert the improper fraction to a rational number. That number is approximately - 1.364. Substitute this number in for x and you will see it checks.

Answer 3

Let n be the number

4n-5=n/3

Just solve for n

Answer 4

4x = (y/3) - 5

Since the problem didn't state that the quotient involved the same number as the product, we need two different variables.

This cannot be solved as it is. Two equations are needed to solve linear equations involving 2 variables. However, the point of such exercises is normally just to translate them into an equation, not to solve them.