If 10 be added to four times a certain number, the result is 5 less than five times the number. Find the number.

Let the required number be x.

"10 added to four times the number" = 4x + 10

"5 less than five times the number" = 5x - 5

According to the given condition we have:

4x + 10 = 5x - 5

⇒ 4x - 5x = - 5 - 10 $\quad$ [Transposing +10 to RHS and +5x to LHS]

⇒ -x = -15

⇒ x = 15

Hence, the required number is 15.