Three real numbers x,y, and z are such that (x+4)/2=(y+9)/(z−3)=(x+5)/(z−5). Determine the value of x/y.
A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.
Solution
Because the first and third fractions are equal, adding their numerators and denominators produces another fraction equal to the others: ((x+4)+(x+5))/(2+(z−5))=(2x+9)/(z−3). Then y+9=2x+9, etc.
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