Question

Daca
$\frac{x}{y} = 45\%$
atunci:
a)
$\frac{y - x}{y} = ...\%$
b)
$\frac{3x +y }{2y} = ...\%$
c)
$\frac{ {x}^{2} }{ {2y}^{2} } = ...\%$


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Answer 1

Explicație pas cu pas:

$\dfrac{x}{y} = 45\% \iff \dfrac{x}{y} = \dfrac{45}{100}$

$\dfrac{x}{y} = \dfrac{9}{20} \iff \dfrac{x}{9} = \dfrac{y}{20} = k$

$x = 9k; \ y = 20k$

a)

$\dfrac{y - x}{y} = \dfrac{20k - 9k}{20k} = \dfrac{11k}{20k} = \dfrac{^{5)} 11}{20} = \dfrac{55}{100} = \bf 55\%$

b)

$\dfrac{3x + y}{2y} = \dfrac{3 \cdot 9k + 20k}{2 \cdot 20k} = \dfrac{27k + 20k}{40k} = \dfrac{47k}{40k} = \dfrac{^{25)} 47}{40} = \dfrac{1175 ^{(10} }{1000} = \dfrac{117.5}{100} = \bf 117.5\%$

c)

$\dfrac{{x}^{2} }{{2y}^{2}} = \dfrac{{(9k)}^{2}}{ {2(20k)}^{2}} = \dfrac{81{k}^{2}}{800 {k}^{2}} = \dfrac{^{125)} 81}{800} = \dfrac{10125^{(1000}}{100000} = \dfrac{10.125}{100} = \bf 10.125\%$