Find the product of two consecutive numbers if four times the first number is 3 more than three times the second number.

Question: Find the product of two consecutive numbers if four times the first number is 3 more than three times the second number.

Solution:
Let the numbers be a and a + 1.
According to the question:
4 × (first number) = 3 × (second number) + 3
⇒ 4a = 3(a + 1) + 3
⇒ 4a = 3a + 3 + 3
⇒ 4a = 3a + 6
⇒ 4a - 3a = 6
⇒ a = 6

∴ The numbers are 6 and 7.
∴ The product of two consecutive numbers = 6 × 7 = 42.