Question

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Answer 1

23) Numa proporção $\dfrac{a}{b}=\dfrac{c}{d}$, vale que, $ad=bc$.

Com os números $3,4,9$ e $12$, podemos formar a proporção $\dfrac{3}{9}=\dfrac{4}{12}$.

Dessa podemos obter outras três: $\dfrac{9}{3}=\dfrac{12}{4}$,  $\dfrac{12}{4}=\dfrac{9}{3}$ e $\dfrac{4}{12}=\dfrac{3}{9}$.


24) 

a)$\dfrac{2}{6}=\dfrac{5}{15}$

Somando os antecedentes e os consequentes: $\dfrac{2+5}{6+15}=\dfrac{7}{21}=\dfrac{2}{6}=\dfrac{5}{15}$

b) $\dfrac{15}{10}=\dfrac{6}{4}$

Subtraindo os antecedentes e os consequentes: $\dfrac{15-6}{10-4}=\dfrac{9}{6}=\dfrac{15}{10}=\dfrac{6}{4}$

25)

a) $\dfrac{10}{x+10}=\dfrac{12}{2x}$

$20x=12x+120$

$8x=120$

$x=15$


b) $\dfrac{x}{4}=\dfrac{y}{6}$

$x+y=15~\Rightarrow~x=15-y$. Substituindo:

$\dfrac{15-y}{4}=\dfrac{y}{6}$

$90-6y=4y$

$10y=90$

$y=9$

$x=15-9=6$


c) $\dfrac{2x}{8}=\dfrac{y}{6}$


$2x-y=3~\Rightarrow~2x=y+3$. Substituindo:

$\dfrac{y+3}{8}=\dfrac{y}{6}$

$6y+18=8y$

$2y=18$

$y=9$

$2x=9+3=12$

$x=6$


d) $\dfrac{x}{y}=\dfrac{9}{6}$


$x+y=35~\Rightarrow~x=35-y$. Substituindo:

$\dfrac{35-y}{y}=\dfrac{9}{6}$

$210-6y=9y$

$15y=210$

$y=14$

$x=35-14=21$

26) 

Meninos -> M
Meninas -> N

$\dfrac{M}{N}=\dfrac{5}{6}$

$M+N=33~\Rightarrow~M=33-N$. Substituindo:

$\dfrac{33-N}{N}=\dfrac{5}{6}$

$198-6N=5N$

$11N=198$

$N=18$

$M=33-18=15$

27)

$\dfrac{x}{y}=\dfrac{1}{4}$

$y=4x$

$x+y=35$. Substituindo:

$x+4x=35$

$5x=35$

$x=7$

$y=4\cdot7=28$

Answer 2

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