Find two consecutive odd numbers such that the sum of one-fifth of the smaller and forth-sevenths of the larger is equal to fifty-nine

Two consecutive odd numbers are 75 and 77.

Step-by-step explanation:

Let's assume the two consecutive odd numbers are A and B such that A > B and their difference is 2, i. e. A - B = 2.

It say the sum of one-fifth of the smaller and forth-sevenths of the larger is equal to fifty-nine, i. e. (4/7) A + (1/5) B = 59.

Simplifying the equation: - 20A + 7B = 2065.

We have a system of equations: - A - B = 2 and 20A + 7B = 2065.

Using Substitution method and substitute A = B + 2 into second equation:-

20 (B+2) + 7B = 2065

20B + 40 + 7B = 2065

27B = 2065-40 = 2025

B = 2025/27 = 225/3 = 75.

Then, A = B+2 = 75+2 = 77.

Hence, two consecutive odd numbers are 75 and 77.