Final answer:
To determine the two numbers algebraically, set up a system of equations. Solve the system to find the two possible pairs of numbers: (64, 46) and (96, 174).
Step-by-step explanation:
To determine the two numbers algebraically, we can set up a system of equations. Let's say the two numbers are x and y. We know that the average of the two numbers is 55, so we can write the equation (x + y) / 2 = 55. We also know that their positive difference is 64, so we can write the equation |x - y| = 64.
To solve this system of equations, we can first isolate one variable in the first equation. By multiplying both sides of the equation by 2, we get x + y = 110. We can then substitute this value into the second equation and solve for the other variable. If we substitute x + y = 110 into the equation |x - y| = 64, we get |110 - y| = 64. Solving this equation gives us two possible values for y: y = 46 or y = 174. Substituting these values back into the first equation, we can find the corresponding values of x: x = 64 or x = 96. Therefore, the two possible pairs of numbers are (64, 46) and (96, 174).