Xiao Yong has a brother and a younger brother. His brother is 20 years old. Twice his brother's age is 97. Xiao Yong's age is 16 and his brother's age is 13. Test center: application of binary linear equation. Special topic: application problem. Analysis: Let's assume that Xiao Yong's age is X, his younger brother's age is Y, and Y is a positive integer, 20 > X > Y ≥ 1. Then get the values of x and y. Solution: Solution: Let Xiao Yong be x years old and his brother be y years old.

Where x and y are positive integers, 20 > x > y ≥ 1, according to the meaning of the question:

2x+5y=97

y= 97-2x5= 20-2x+35

Because y is a positive integer, 2x+35 is also a positive integer, 1 < x < 20, x is a positive integer, x > y；;

According to x > y, we can get 20-2x+35 < x, x > 1367.

∴20>x≥ 14

① When x= 14, 15, it is irrelevant;

② When x= 16, y =13;

③ When x= 17, 18, 19, it is irrelevant.

Therefore, only when x= 16 and y= 13 can the problem be satisfied.

So the answer is 16, 13.