Final answer:
To solve this problem, set up the equation x/3 - 11 = 19 and solve for x. The number you are looking for is 90.
Step-by-step explanation:
To solve this problem, we need to set up an equation based on the given information and then solve for the unknown number. Let's define the number as 'x'. The quotient of a number and 3 can be expressed as x/3. And 11 less than the quotient is x/3 - 11. According to the problem, this expression is equal to 19. So, we have the equation:
x/3 - 11 = 19
To find the value of x, we can start by adding 11 to both sides of the equation to isolate the x/3 term:
x/3 - 11 + 11 = 19 + 11
x/3 = 30
To get rid of the fraction, we can multiply both sides of the equation by 3:
3 * (x/3) = 3 * 30
x = 90
Therefore, the number we are looking for is 90.