the product of a number and 2 is 5 less than the quotient of a number and 3

Question

the product of a number and 2 is 5 less than the quotient of a number and 3

Answer 1

The sentence you have can be expressed in algebra (using x as 'the number'):

 

2x + 5 = x / 3.  (We add 5 to the left side because that product is less than the right side.)

 

Now all you have to do is to combine the x terms on one side of equation, putting the constant on the other side of the equation, and solve for x.

 

There you go! 

Answer 2

Let the unknown number that we are solving for be x.

 

The product of a number and 2  means 2*x 

 

5 less than the quotient of a number and 3 means x/3 - 5.

 

 So, 

 

  2*x = x/3 - 5   subtract x/3 from both sides of the equation

 

 2x - x/3 = -5 , now find the least common denominator for the left side of the equation

 

6x/3 - x/3 = -5

 

(6x - x)/3 = -5

 

5x/3       = -5, now multiply both sides of the equation by 3

 

5x          = -15  now divide both sides of the equation by 5

 

x = - 3. So the number is -3.