Question

Aplicando as propriedades da proporçao, calcule x e y :
A) x+y=27
x/y=2/7

B) x+y=20
x/2=y/3

Answer 1

.
$A) \\ ~~ \frac{x}{y} = \frac{2}{7} ~~~~~~~~~x+y=27 \\ \\ \frac{x+y}{x} = \frac{2+7}{2} ~~~~~~~~~~~~~~ \frac{x+y}{y} = \frac{2+7}{7} \\ \\ \frac{27}{x} = \frac{9}{2} ~~~~~~~~~~~~~~~~~~~~ \frac{27}{y} = \frac{9}{7} \\ \\ 9x=54~~~~~~~~~~~~~~~~~~~~9x=189 \\ \\ x=54\div9~~~~~~~~~~~~~~~~~y=189\div9 \\ \\ x=6~~~~~~~~~~~~~~~~~~~~~~~y= 21$
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B)
$\frac{x}{2} = \frac{y}{3} ~~~~~~~~~~~~~~x+y=20 \\ \\ \frac{x+y}{2+3} = \frac{x}{2} ~~~~~~~~~~~~~~~~ \frac{20}{5} = \frac{y}{3} \\ \\ \frac{20}{5} = \frac{x}{2} ~~~~~~~~~~~~~~~~~~~~5y=60 \\ \\ 5x=40~~~~~~~~~~~~~~~~~~y=60\div5 \\ \\ x=40\div5~~~~~~~~~~~~~~~y=12 \\ \\ x=8$