1 -
a)
[tex] \frac{x}{5} = \frac{21}{35} \div 7 \\ \frac{x}{5} = \frac{3}{5} \\ 5x = 3 \times 5 \\ x = \frac{15}{5} = 3[/tex]
b)
[tex] \frac{10}{7} = \frac{50}{x} \\ 10x = 50 \times 7 \\ 10x = 350 \\ x = \frac{350}{10} = 35[/tex]
c)
[tex] \frac{1}{7} = \frac{ \times - 6}{49} \\ 7 \times (x - 6) = 49 \\ 7x - 42 = 49 \\ 7x = 49 + 42 \\ x = \frac{91}{7} = 13[/tex]
d)
[tex] \frac{5x + 3}{10} = \frac{ - 21}{30} \\ 30\times (5x + 3) = 10 \times (- 21) \\ 150x + 90 = - 210 \\ 150x = - 210 - 90 \\ x = \frac{ - 300}{150} = - 2[/tex]
e)
[tex] \frac{5}{ x + 4} = \frac{30}{54} \div 6 \\ \frac{5}{x + 4} = \frac{5}{9} \\ 5 \times (x + 4) = 45 \\ 5x + 20 = 45 \\ 5x = 45 - 20 \\ x = \frac{25}{5} = 5[/tex]
f)
[tex] \frac{0.9}{x} = \frac{ - 18}{27} \div 9 \\ \frac{0.9}{x} = \frac{ - 2}{3} \\ - 2x = 3 \times 0.9 \\ x = \frac{2.7}{ - 2} = - 1.35[/tex]
g)
[tex] \frac{7x + 5}{4} = \frac{2x}{ \frac{3}{4} } \\ \frac{7x + 5}{4} = \frac{2x}{1} \times \frac{4}{3 } \\ \frac{7x + 5}{4} = \frac{8x}{3} \\ 3 \times (7x + 5) = 8x \times 4 \\ 21x + 15 = 32x \\ x = \frac{15}{11} = 1.36[/tex]
2 -
[tex]x + y = 42 \\ \frac{x}{y} = \frac{5}{9} \\ \frac{x + y}{y} = \frac{5 + 9}{9} \\ \frac{42}{y} = \frac{14}{9} \\ 14y = 9 \times 42 \\ y = \frac{378}{14} = 27 \\ x = 42 - 27 = 15[/tex]
3 -
[tex]a + b = 55 \\ \frac{a}{b} = \frac{4}{7} \\ \frac{a + b}{b} = \frac{4 + 7}{7} \\ \frac{55}{b} = \frac{11}{7} \\ 11b = 55 \times 7 \\ b = \frac{385}{11} = 35 \\ a = 55 - 35 = 20[/tex]
4 -
[tex]p + f = 45 \\ \frac{p}{f} = \frac{7}{2} \\ \frac{p + f}{f} = \frac{7 + 2}{2} \\ \frac{45}{f} = \frac{9}{2} \\ 9f = 45 \times 2 \\ f = \frac{90}{9} = 10anos \\ p = 45 - 10 = 35anos[/tex]
