Ashley is 15 years younger than jessica. if the sum of their ages is 71, how old are they

The first thing we must do for this case is to define variables.
 We have then:
 x = Ashley age
 y = Jessica age
 We write the system of equations:
 x + y = 71
 x = y-15
 Solving the system we have:
 (y-15) + y = 71
 2y - 15 = 71
 y = (71 + 15) / (2)
 y = 43 years
 Then, for x we have:
 x = y-15
 x = 43-15
 x = 28 years
 
 Ashley is 28 years old.
 Jessica is 43 years old.

Let
x> Ashley ages
y> Jessica ages

we know that
x=y-15> equation 1
x+y=71> equation 2

(y-15)+y=71> 2y=71+15> y=86/2> y=43
x=y-15> x=43-15> x=28

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