Short Answer 
To find the unknown number that equals 17 when three-fourths of it is considered, we set up the equation (3/4)x = 17. By multiplying both sides by the reciprocal (4/3), we calculate x, yielding the solution of approximately 22.67.
a) Finding the Number
To determine the unknown number when three-fourths of it equals 17, first, you must understand the problem scenario. You need to express this relationship mathematically. This leads us to formulate an equation representing this relationship.
- We denote the unknown number as x.
- The equation becomes: (3/4) √ó x = 17.
b) Establishing the Equation
Next, set up the equation based on the known relationship. We want to isolate the variable to determine the total quantity. To achieve this, multiply both sides by the reciprocal of the fraction in the equation.
- The reciprocal of (3/4) is (4/3).
- The modified equation is: x = 17 √ó (4/3).
c) Solving for the Unknown
Finally, perform the calculations to solve for the unknown variable. You multiply the values to find the result. This gives you the approximate value of the number in question.
- Calculating gives: x = 22.67.
- This means three-fourths of the number is indeed equal to 17, confirming that the full number is approximately 22.67.