(4 1/6 у + 11 1/4) × 4/15 = 2/3у + 5 2/3

(4 1/6у + 11 1/4) * 4/15 = 2/3у + 5 2/3;

Представим дроби с целой частью в виде неправильных дробей:

(25/6у + 45/4) * 4/15 = 2/3у + 17/3;

25/6у * 4/15 + 45/4 * 4/15 = 2/3у + 17/3;

10/9у + 3 = 2/3у + 17/3;

10/9у - 2/3у = 17/3 - 3;

10/9у - 6/9у = 17/3 - 9/3;

4/9у = 8/3;

у = 8/3 : 4/9;

у = 8/3 * 9/4;

у = 6.

Проверка:

(4 1/6 * 6 + 11 1/4) * 4/15 = 2/3 * 6 + 5 2/3;

(25/6 * 6 + 45/4) * 4/15 = 2/3 * 6 + 17/3;

(25 + 45/4) * 4/15 = 4 + 17/3;

(100/4 + 45/4) * 4/15 = 12/3 + 17/3;

145/4 * 4/15 = 29/3;

29/3 = 29/3.

Ответ: у = 6.