Question

of the two numbers, 4 times the smaller one is less than 3 times the larger one by 6. Also,
the sum of the numbers is larger than 6 times their difference by 5. Find the numbers.​

Answer 1

Answer: 45/13

Step-by-step explanation: Let the smaller number be X and the larger number be Y. Then -

According to question, 4x + 6 = 3y

                                Also, x + y = 6(x - y) + 5

                                     ⇒ x + y = 6x - 6y + 5

From the first equation , we get - y = (4x + 6)/3

So in the second equation, we have x + (4x + 6)/3 = 6x - 2(4x - 6) + 5

                                                          ⇒ (3x + 4x + 6)/3 = 6x - 8x + 12 + 5

                                                          ⇒ 7x + 6/3 = -2x + 17

                                                          ⇒ 7x + 6 = -6x + 51

                                                          ⇒ 13x = 45

                                                           ⇒ x = 45/13