3. Для натуральных чисел х, у и z выполняется равенство 2x+4y+z=75. Найдите максимально возможное значение х A) 34 B) 35 C) 36 D) 37 E) 38​

Відповідь:

35

Покрокове пояснення:

2x+4y+z=75натуральні числа починаються від 1тому найбільше значення х може досягається коли у та z дорывнюють 1 2x+4y+z=752x+4*1+1=75

2x=70

x=35

Все валидные пары (x, y, z):

(0, 0, 75)

(0, 1, 71)

(0, 2, 67)

(0, 3, 63)

(0, 4, 59)

(0, 5, 55)

(0, 6, 51)

(0, 7, 47)

(0, 8, 43)

(0, 9, 39)

(0, 10, 35)

(0, 11, 31)

(0, 12, 27)

(0, 13, 23)

(0, 14, 19)

(0, 15, 15)

(0, 16, 11)

(0, 17, 7)

(0, 18, 3)

(1, 0, 73)

(1, 1, 69)

(1, 2, 65)

(1, 3, 61)

(1, 4, 57)

(1, 5, 53)

(1, 6, 49)

(1, 7, 45)

(1, 8, 41)

(1, 9, 37)

(1, 10, 33)

(1, 11, 29)

(1, 12, 25)

(1, 13, 21)

(1, 14, 17)

(1, 15, 13)

(1, 16, 9)

(1, 17, 5)

(1, 18, 1)

(2, 0, 71)

(2, 1, 67)

(2, 2, 63)

(2, 3, 59)

(2, 4, 55)

(2, 5, 51)

(2, 6, 47)

(2, 7, 43)

(2, 8, 39)

(2, 9, 35)

(2, 10, 31)

(2, 11, 27)

(2, 12, 23)

(2, 13, 19)

(2, 14, 15)

(2, 15, 11)

(2, 16, 7)

(2, 17, 3)

(3, 0, 69)

(3, 1, 65)

(3, 2, 61)

(3, 3, 57)

(3, 4, 53)

(3, 5, 49)

(3, 6, 45)

(3, 7, 41)

(3, 8, 37)

(3, 9, 33)

(3, 10, 29)

(3, 11, 25)

(3, 12, 21)

(3, 13, 17)

(3, 14, 13)

(3, 15, 9)

(3, 16, 5)

(3, 17, 1)

(4, 0, 67)

(4, 1, 63)

(4, 2, 59)

(4, 3, 55)

(4, 4, 51)

(4, 5, 47)

(4, 6, 43)

(4, 7, 39)

(4, 8, 35)

(4, 9, 31)

(4, 10, 27)

(4, 11, 23)

(4, 12, 19)

(4, 13, 15)

(4, 14, 11)

(4, 15, 7)

(4, 16, 3)

(5, 0, 65)

(5, 1, 61)

(5, 2, 57)

(5, 3, 53)

(5, 4, 49)

(5, 5, 45)

(5, 6, 41)

(5, 7, 37)

(5, 8, 33)

(5, 9, 29)

(5, 10, 25)

(5, 11, 21)

(5, 12, 17)

(5, 13, 13)

(5, 14, 9)

(5, 15, 5)

(5, 16, 1)

(6, 0, 63)

(6, 1, 59)

(6, 2, 55)

(6, 3, 51)

(6, 4, 47)

(6, 5, 43)

(6, 6, 39)

(6, 7, 35)

(6, 8, 31)

(6, 9, 27)

(6, 10, 23)

(6, 11, 19)

(6, 12, 15)

(6, 13, 11)

(6, 14, 7)

(6, 15, 3)

(7, 0, 61)

(7, 1, 57)

(7, 2, 53)

(7, 3, 49)

(7, 4, 45)

(7, 5, 41)

(7, 6, 37)

(7, 7, 33)

(7, 8, 29)

(7, 9, 25)

(7, 10, 21)

(7, 11, 17)

(7, 12, 13)

(7, 13, 9)

(7, 14, 5)

(7, 15, 1)

(8, 0, 59)

(8, 1, 55)

(8, 2, 51)

(8, 3, 47)

(8, 4, 43)

(8, 5, 39)

(8, 6, 35)

(8, 7, 31)

(8, 8, 27)

(8, 9, 23)

(8, 10, 19)

(8, 11, 15)

(8, 12, 11)

(8, 13, 7)

(8, 14, 3)

(9, 0, 57)

(9, 1, 53)

(9, 2, 49)

(9, 3, 45)

(9, 4, 41)

(9, 5, 37)

(9, 6, 33)

(9, 7, 29)

(9, 8, 25)

(9, 9, 21)

(9, 10, 17)

(9, 11, 13)

(9, 12, 9)

(9, 13, 5)

(9, 14, 1)

(10, 0, 55)

(10, 1, 51)

(10, 2, 47)

(10, 3, 43)

(10, 4, 39)

(10, 5, 35)

(10, 6, 31)

(10, 7, 27)

(10, 8, 23)

(10, 9, 19)

(10, 10, 15)

(10, 11, 11)

(10, 12, 7)

(10, 13, 3)

(11, 0, 53)

(11, 1, 49)

(11, 2, 45)

(11, 3, 41)

(11, 4, 37)

(11, 5, 33)

(11, 6, 29)

(11, 7, 25)

(11, 8, 21)

(11, 9, 17)

(11, 10, 13)

(11, 11, 9)

(11, 12, 5)

(11, 13, 1)

(12, 0, 51)

(12, 1, 47)

(12, 2, 43)

(12, 3, 39)

(12, 4, 35)

(12, 5, 31)

(12, 6, 27)

(12, 7, 23)

(12, 8, 19)

(12, 9, 15)

(12, 10, 11)

(12, 11, 7)

(12, 12, 3)

(13, 0, 49)

(13, 1, 45)

(13, 2, 41)

(13, 3, 37)

(13, 4, 33)

(13, 5, 29)

(13, 6, 25)

(13, 7, 21)

(13, 8, 17)

(13, 9, 13)

(13, 10, 9)

(13, 11, 5)

(13, 12, 1)

(14, 0, 47)

(14, 1, 43)

(14, 2, 39)

(14, 3, 35)

(14, 4, 31)

(14, 5, 27)

(14, 6, 23)

(14, 7, 19)

(14, 8, 15)

(14, 9, 11)

(14, 10, 7)

(14, 11, 3)

(15, 0, 45)

(15, 1, 41)

(15, 2, 37)

(15, 3, 33)

(15, 4, 29)

(15, 5, 25)

(15, 6, 21)

(15, 7, 17)

(15, 8, 13)

(15, 9, 9)

(15, 10, 5)

(15, 11, 1)

(16, 0, 43)

(16, 1, 39)

(16, 2, 35)

(16, 3, 31)

(16, 4, 27)

(16, 5, 23)

(16, 6, 19)

(16, 7, 15)

(16, 8, 11)

(16, 9, 7)

(16, 10, 3)

(17, 0, 41)

(17, 1, 37)

(17, 2, 33)

(17, 3, 29)

(17, 4, 25)

(17, 5, 21)

(17, 6, 17)

(17, 7, 13)

(17, 8, 9)

(17, 9, 5)

(17, 10, 1)

(18, 0, 39)

(18, 1, 35)

(18, 2, 31)

(18, 3, 27)

(18, 4, 23)

(18, 5, 19)

(18, 6, 15)

(18, 7, 11)

(18, 8, 7)

(18, 9, 3)

(19, 0, 37)

(19, 1, 33)

(19, 2, 29)

(19, 3, 25)

(19, 4, 21)

(19, 5, 17)

(19, 6, 13)

(19, 7, 9)

(19, 8, 5)

(19, 9, 1)

(20, 0, 35)

(20, 1, 31)

(20, 2, 27)

(20, 3, 23)

(20, 4, 19)

(20, 5, 15)

(20, 6, 11)

(20, 7, 7)

(20, 8, 3)

(21, 0, 33)

(21, 1, 29)

(21, 2, 25)

(21, 3, 21)

(21, 4, 17)

(21, 5, 13)

(21, 6, 9)

(21, 7, 5)

(21, 8, 1)

(22, 0, 31)

(22, 1, 27)

(22, 2, 23)

(22, 3, 19)

(22, 4, 15)

(22, 5, 11)

(22, 6, 7)

(22, 7, 3)

(23, 0, 29)

(23, 1, 25)

(23, 2, 21)

(23, 3, 17)

(23, 4, 13)

(23, 5, 9)

(23, 6, 5)

(23, 7, 1)

(24, 0, 27)

(24, 1, 23)

(24, 2, 19)

(24, 3, 15)

(24, 4, 11)

(24, 5, 7)

(24, 6, 3)

(25, 0, 25)

(25, 1, 21)

(25, 2, 17)

(25, 3, 13)

(25, 4, 9)

(25, 5, 5)

(25, 6, 1)

(26, 0, 23)

(26, 1, 19)

(26, 2, 15)

(26, 3, 11)

(26, 4, 7)

(26, 5, 3)

(27, 0, 21)

(27, 1, 17)

(27, 2, 13)

(27, 3, 9)

(27, 4, 5)

(27, 5, 1)

(28, 0, 19)

(28, 1, 15)

(28, 2, 11)

(28, 3, 7)

(28, 4, 3)

(29, 0, 17)

(29, 1, 13)

(29, 2, 9)

(29, 3, 5)

(29, 4, 1)

(30, 0, 15)

(30, 1, 11)

(30, 2, 7)

(30, 3, 3)

(31, 0, 13)

(31, 1, 9)

(31, 2, 5)

(31, 3, 1)

(32, 0, 11)

(32, 1, 7)

(32, 2, 3)

(33, 0, 9)

(33, 1, 5)

(33, 2, 1)

(34, 0, 7)

(34, 1, 3)

(35, 0, 5)

(35, 1, 1)

(36, 0, 3)

(37, 0, 1)

Максимальное возможное значение х это 37