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The prices of two radios are in the ration x : y
When the prices are both increased be £20, the ratio becomes 5 : 2
When the prices are both reduces by £5, the ratio becomes 5 : 1
Express the ratio x : y in it’s lowest terms.

Respuesta :

[tex]\bf x:y\qquad \qquad \qquad \stackrel{x+20}{5}:\stackrel{y+20}{2}\qquad \qquad \qquad \stackrel{x-5}{5}:\stackrel{y-5}{1}\\\\ -------------------------------\\\\ \cfrac{x+20}{y+20}=\cfrac{5}{2}\implies 2x+40=5y+100\implies 2x-60=5y \\\\\\ \boxed{\cfrac{2x-60}{5}=y}[/tex]

[tex]\bf \cfrac{x-5}{y-5}=\cfrac{5}{1}\implies x-5=5y-25\implies x-5=5\left( \boxed{\cfrac{2x-60}{5}} \right)-25 \\\\\\ x-5=2x-60-25\implies x-5=2x-85\implies \underline{80=x} \\\\\\ \cfrac{2x-60}{5}=y\implies \cfrac{2(80)-60}{5}=y\implies \cfrac{100}{5}=y\implies \underline{20=y}\\\\ -------------------------------\\\\ x:y\implies \cfrac{x}{y}\implies \cfrac{80}{20}\implies \cfrac{4}{1}[/tex]

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