pensei em dois numeros cuja diferença é 49 e a razao do menor para o maior é 2/9.Em que numero pensei..com cálculo
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Devemos fazer uma sistema de equações: Assim:
![\left \{ {{x - y = 49} \atop { \frac{x}{y} = \frac{2}{9} }} \right. \\\\
I- \ \ x - y = 49 \\
I- \ \boxed{ x = 49 \ + \ y} \\\\
\frac{x}{y} = \frac{2}{9} \\\\
\frac{49 \ + \ y}{y} = \frac{2}{9} \\\\
(49 \ + \ y) \ * \ 9 = 2 * y \\\\
441 + 9y = 2y \\\\
9y - 2y = -441 \\\\
7y = -441 \\\\
y = \frac{-441}{7} \\\\
\boxed{y = -63} \\\\\\\
I- \ \ \ x = 49 + y \\\\
x = 49 + (-63) \\\\
x = 49 -63 \\\\
\boxed{x = -14}](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bx+-+y+%3D+49%7D+%5Catop+%7B+%5Cfrac%7Bx%7D%7By%7D+%3D+%5Cfrac%7B2%7D%7B9%7D+%7D%7D+%5Cright.+%5C%5C%5C%5C%0AI-+++%5C+%5C+x+-+y+%3D+49+%5C%5C+%0AI-+++%5C+%5Cboxed%7B+x+%3D+49+%5C+%2B+%5C+y%7D+%5C%5C%5C%5C+%0A%5Cfrac%7Bx%7D%7By%7D+%3D++%5Cfrac%7B2%7D%7B9%7D+%5C%5C%5C%5C+%0A+%5Cfrac%7B49+%5C+%2B+%5C+y%7D%7By%7D+%3D++%5Cfrac%7B2%7D%7B9%7D+%5C%5C%5C%5C%0A+%2849+%5C+%2B+%5C+y%29+%5C+%2A+%5C+9+%3D++2+%2A+y+%5C%5C%5C%5C%0A441++%2B+9y+%3D+2y+%5C%5C%5C%5C+%0A9y+-+2y+%3D+-441+%5C%5C%5C%5C%0A7y+%3D+-441+%5C%5C%5C%5C+%0Ay+%3D++%5Cfrac%7B-441%7D%7B7%7D+%5C%5C%5C%5C+%0A%5Cboxed%7By+%3D+-63%7D+%5C%5C%5C%5C%5C%5C%5C+%0AI-+%5C+%5C+%5C+x+%3D+49+%2B+y+%5C%5C%5C%5C+%0Ax+%3D+49+%2B+%28-63%29+%5C%5C%5C%5C+%0Ax+%3D+49+-63+%5C%5C%5C%5C%0A%5Cboxed%7Bx+%3D+-14%7D "\left \{ {{x - y = 49} \atop { \frac{x}{y} = \frac{2}{9} }} \right. \\\\
I- \ \ x - y = 49 \\
I- \ \boxed{ x = 49 \ + \ y} \\\\
\frac{x}{y} = \frac{2}{9} \\\\
\frac{49 \ + \ y}{y} = \frac{2}{9} \\\\
(49 \ + \ y) \ * \ 9 = 2 * y \\\\
441 + 9y = 2y \\\\
9y - 2y = -441 \\\\
7y = -441 \\\\
y = \frac{-441}{7} \\\\
\boxed{y = -63} \\\\\\\
I- \ \ \ x = 49 + y \\\\
x = 49 + (-63) \\\\
x = 49 -63 \\\\
\boxed{x = -14}")
Portanto esse números são 14 e 63.
Portanto esse números são 14 e 63.
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