Question

when 5 times the larger of the two numbers is divided by the smaller, the quotient and remainder are 2 & 9 respectively. Form a linear equation into variables for above and give its two solutions.

Answer 1

Let the larger number be x and smaller number be y Five times larger number = 5x When 5x is divided by y the quotient is 2 and remainder is 9. By division rule, we have Dividend = (divisor) × (quotient) + Remainder 5x = y(2) + 9 ⇒ 5x – 2y – 9 = 0Put x = 3 and y = 3 in LHS 5x – 2y – 9
= 5(3) – 2(3) – 9                   = 15 – 15 = 0                  = RHS Hence x = 3 and y = 3 is one of the solution of the linear equation.