Final answer:
The product of the two numbers, where one number is 2/3 of the other and one-third of their sum is 5/6, is 3/2.
Step-by-step explanation:
Let's denote the first number as X and the second number as Y. Given that one number is 2/3 of another number, we can write the equation Y = (2/3)X. Additionally, it is given that one-third of the sum of the two numbers is 5/6. So, we write the equation (1/3)(X + Y) = 5/6. Multiplying both sides by 3 to get rid of the fraction, we get X + Y = 5/2.
Now, substituting Y from the first equation into the second equation, we obtain X + (2/3)X = 5/2. Combining like terms, we have (5/3)X = 5/2. Solving for X, we multiply both sides by the reciprocal of (5/3), which is (3/5), yielding X = (3/5) × (5/2) = 3/2. Now, we can find Y by plugging X back into the first equation: Y = (2/3) × (3/2) = 1.
The product of the two numbers is therefore X × Y, which equates to (3/2) × 1 = 3/2.