The combined age of three sisters is 74. The eldest sisters age is twelve less than the sum of both sisters age. The middle sister is 5 years older than the youngest. What is the age of each sister?

Step-by-step explanation:

let their ages be x, y, z and x>y>z

x+y+z=74 ... (1)

x = (y+z) - 12

or x-y-z=-12 ... (2)

y=z+5 ... (3)

add (1) and (2)

2x=62

x=62/2=31

from (1)

31+y+z=74

y+z=74-31=43

substitute from (3)

z+5+z=43

2z=43-5=38

z=38/2=19

y=19+5=24

so their ages are 31,24 and 19