Kolme numbri summa on 100. Suuremate kahe erinevus on 12 ja väiksemate kahe erinevus on 2. Mis on arvud?


Vastus 1:

Numbrid on 28, 30 ja 42.

Olgu kolm numbrit a, b ja c. Antud tingimused on järgmised:

  • a + b + c = 100b-a = 2või b = 2 + ac-b = 12või c = 12 + bor c = 12 + (2 + a) c = 14 + a

Nii et lahendage a jaoks.

  • a + b + c = 100a + 2 + a + 14 + a = 1003a + 16–16 = 100–163a ÷ 3 = 84 ÷ 3a = 28

Nüüd saada väärtus b.

  • b = 2 + ab = 2 + 28b = 30

Lõpuks saada väärtus c.

  • ja c = 14 + 14 = 42 + 28c =

Seega on numbrid 28, 30 ja 42.

Kontrollimine:

  • 28 + 30 + 42 = 10042–30 = 1230–28 = 24

Vastus 2:

Let the numbers be x, y and z withx>y>zthen\text{Let the numbers be x, y and z with}\,\,x\gt y\gt z\,\,\text{then}

x+y+z=100xy=12yz=2x + y + z = 100\qquad x - y = 12\qquad y - z = 2

x+y+z=100x + y + z = 100

    (xy)(yz)+3y=100\implies (x - y) - (y - z) + 3 y = 100

    122+3y=100\implies 12 - 2 + 3 y = 100

    3y=90    y=30\implies 3 y = 90\implies y = 30

xy=12    x30=12    x=42x - y = 12\implies x - 30 = 12\implies x = 42

yz=2    30z=2    z=302=28y - z = 2\implies 30 - z = 2\implies z = 30 - 2 = 28


Vastus 3:

Let the numbers be x, y and z withx>y>zthen\text{Let the numbers be x, y and z with}\,\,x\gt y\gt z\,\,\text{then}

x+y+z=100xy=12yz=2x + y + z = 100\qquad x - y = 12\qquad y - z = 2

x+y+z=100x + y + z = 100

    (xy)(yz)+3y=100\implies (x - y) - (y - z) + 3 y = 100

    122+3y=100\implies 12 - 2 + 3 y = 100

    3y=90    y=30\implies 3 y = 90\implies y = 30

xy=12    x30=12    x=42x - y = 12\implies x - 30 = 12\implies x = 42

yz=2    30z=2    z=302=28y - z = 2\implies 30 - z = 2\implies z = 30 - 2 = 28


Vastus 4:

Let the numbers be x, y and z withx>y>zthen\text{Let the numbers be x, y and z with}\,\,x\gt y\gt z\,\,\text{then}

x+y+z=100xy=12yz=2x + y + z = 100\qquad x - y = 12\qquad y - z = 2

x+y+z=100x + y + z = 100

    (xy)(yz)+3y=100\implies (x - y) - (y - z) + 3 y = 100

    122+3y=100\implies 12 - 2 + 3 y = 100

    3y=90    y=30\implies 3 y = 90\implies y = 30

xy=12    x30=12    x=42x - y = 12\implies x - 30 = 12\implies x = 42

yz=2    30z=2    z=302=28y - z = 2\implies 30 - z = 2\implies z = 30 - 2 = 28