This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Define the unknown number. Let the number be x. Step 2: Translate the first part of the statement into an algebraic expression. "(3)/(4) of a number is added to (5)/(6)" can be written as: (3)/(4)x + (5)/(6) Step 3: Translate the second part of the statement into an algebraic expression. "(7)/(8) subtracted from the number" can be written as: x - (7)/(8) Step 4: Set up the equation based on the problem statement. The problem states that the results from Step 2 and Step 3 are the same: (3)/(4)x + (5)/(6) = x - (7)/(8) Step 5: Solve the equation for x. To eliminate the denominators, find the least common multiple (LCM) of 4, 6, and 8. The LCM of 4, 6, and 8 is 24. Multiply every term in the equation by 24: 24 ((3)/(4)x) + 24 ((5)/(6)) = 24(x) - 24 ((7)/(8)) 6(3x) + 4(5) = 24x - 3(7) 18x + 20 = 24x - 21 Step 6: Gather x terms on one side and constant terms on the other side. Subtract 18x from both sides: 20 = 24x - 18x - 21 20 = 6x - 21 Add 21 to both sides: 20 + 21 = 6x 41 = 6x Step 7: Isolate x. Divide by 6: x = (41)/(6) The number is (41)/(6).