The sum of 2 consecutive whole numbers is $\frac{5}{6}$ of their product, find the numbers

Analyze the question: We need two consecutive whole numbers whose sum equals 5/6 of their product.

Set up: Let the numbers be n and n + 1.

• Sum = n + (n + 1) = 2n + 1
• Product = n(n + 1)

Condition: 2n + 1 = (5/6) · n(n + 1)

Solve:

Multiply both sides by 6: 12n + 6 = 5n² + 5n

Rearrange: 5n² − 7n − 6 = 0

Factorise (find two numbers that multiply to −30 and add to −7: −10 and 3): 5n² − 10n + 3n − 6 = 0 5n(n − 2) + 3(n − 2) = 0 (5n + 3)(n − 2) = 0

So n = 2 or n = −3/5. Since n must be a whole number, n = 2, and the numbers are 2 and 3.

Check:

• Sum = 2 + 3 = 5
• Product = 6, and 5/6 of 6 = 5 ✓

Checking the other options:

• A (3, 4): sum 7, product 12, 5/6 × 12 = 10 ≠ 7 ✗
• B (1, 2): sum 3, product 2, 5/6 × 2 = 5/3 ≠ 3 ✗
• D (0, 1): sum 1, product 0, 5/6 × 0 = 0 ≠ 1 ✗

Tip: In multiple-choice questions like this, you can quickly test each option by substituting it. Here, the sum must be smaller than the product, and the product 6 being divisible by 6 makes (2, 3) an obvious candidate, since 5/6 of 6 is a whole number.