Question

Using properties of proportion find x:y if 9x + 14y: 9x-14y = 9:7.​

Answer 1

SOLUTION

GIVEN

$\displaystyle \sf{(9x + 14y) : (9x - 14y) = 9 :7 }$

TO DETERMINE

The value of x : y

EVALUATION

$\displaystyle \sf{(9x + 14y) : (9x - 14y) = 9 :7 }$

$\displaystyle \sf{ \implies \: \frac{(9x + 14y)}{(9x - 14y)} = \frac{9}{7} }$

By Componendo - Dividendo rule we get

$\displaystyle \sf{ \implies \: \frac{(9x + 14y )+ (9x - 14y)}{(9x + 14y) - (9x - 14y)} = \frac{9 + 7}{9 - 7} }$

$\displaystyle \sf{ \implies \: \frac{18x}{28y} = \frac{16}{2} }$

$\displaystyle \sf{ \implies \: \frac{18x}{28y} = 8 }$

$\displaystyle \sf{ \implies \: \frac{9x}{14y} = 8 }$

$\displaystyle \sf{ \implies \: \frac{x}{y} = \frac{112}{9} }$

$\displaystyle \sf{ \implies x: y =1 12 : 9}$

FINAL ANSWER

$\displaystyle \sf{ x: y = 112 : 9}$

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