What is x in the following ration equation $\Rightarrow x : (\frac{23}{42} + x) = \frac{8}{25} : \frac{14}{15}$ $=> x:(23/42 +x)=8/25 : 14/15$ ?

Question

What is x in the following ration equation: $x : (\frac{23}{42} + x) = \frac{8}{25} : \frac{14}{15}$ $x:(23/42 +x)=8/25 : 14/15$ ?

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Answer 1 · 2016-04-27T06:06:43

$x = \frac{2}{7}$ $x=2/7$

If $a : b = c : d$ $a:b=c:d$ then $a \times d = b \times c$ $axxd=bxxc$ , hence

$x \times \frac{14}{15} = (\frac{23}{42} + x) \times \frac{8}{25}$ $x xx14/15=(23/42+x)xx8/25$

or multiplying both sides by $\frac{25}{8}$ $25/8$

$\frac{14 x}{15} \times \frac{25}{8} = \frac{23}{42} + x$ $(14x)/15xx25/8=23/42+x$

or
$(7cancel14x)/(3cancel15)xx(5cancel25)/(4cancel8)=23/42+x$

$(35x)/12=23/42+x$ or

$(35x)/12-x=(35x)/12-(12x)/12=23/42$

or $(23x)/12=23/42$

or $x=cancel23/(7cancel42)xx(2cancel12)/cancel23$

or $x=2/7$