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: Represent the two numbers using the given ratio. Let the two positive numbers be 3x and 4x, where x is a common factor. Step 2: Formulate an equation based on the second condition. "The sum of thrice the first number and twice the second is 68." Thrice the first number is 3(3x) = 9x. Twice the second number is 2(4x) = 8x. Their sum is 68: 9x + 8x = 68 Step 3: Solve the equation for x. 17x = 68 x = (68)/(17) x = 4 Step 4: Find the two numbers. The first number is 3x = 3(4) = 12. The second number is 4x = 4(4) = 16. Step 5: Identify the smaller number. Comparing 12 and 16, the smaller number is 12. The final answer is 12. That's 2 down. 3 left today — send the next one.