Els números són 28, 30 i 42.

Siguin els tres nombres a, b i c. Les condicions donades són:

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

Per tant, resolgui per a.

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

Obteniu el valor per a b.

• b = 2 + ab = 2 + 28b = 30

Finalment, obteniu el valor de c.

• i c = 14 + 14 = 42 + 28c =

Així, els nombres són 28, 30 i 42.

Verificació:

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

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

$x + y + z = 100\qquad x - y = 12\qquad y - z = 2$

$x + y + z = 100$

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

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

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

$x - y = 12\implies x - 30 = 12\implies x = 42$

$y - z = 2\implies 30 - z = 2\implies z = 30 - 2 = 28$

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

$x + y + z = 100\qquad x - y = 12\qquad y - z = 2$

$x + y + z = 100$

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

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

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

$x - y = 12\implies x - 30 = 12\implies x = 42$

$y - z = 2\implies 30 - z = 2\implies z = 30 - 2 = 28$

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

$x + y + z = 100\qquad x - y = 12\qquad y - z = 2$

$x + y + z = 100$

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

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

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

$x - y = 12\implies x - 30 = 12\implies x = 42$

$y - z = 2\implies 30 - z = 2\implies z = 30 - 2 = 28$