Find the product of two consecutive numbers if three times the first number is 5 more than twice the second number.

Question: Find the product of two consecutive numbers if three times the first number is 5 more than twice the second number.

Solution:
Let the numbers be a and a + 1.

According to the question:
3 × (first number) = 2 × (second number) + 5
⇒ 3a = 2(a + 1) + 5
⇒ 3a = 2a + 2 + 5
⇒ 3a = 2a + 7
⇒ 3a - 2a = 7
⇒ a = 7

∴ The numbers are 7 and 8.
Product = 7 × 8 = 56