Question 506293: Jean is 27 years older than her daughter Rita. After 8 years she will be twice as old as Rita. Find their present ages. Answer by Maths68(1474) (Show Source):
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Present age of Jean = j
Present age of Rita = r
Jean is 27 years older than her daughter Rita means if we add 27 to Rita's present both mother and daughter will be of equal age
j=r+27 ............(1)
After 8 years means we have to add 8 in their present ages
j+8=r+8
then
Jean will be twice as old as Rita
j+8=2*(r+8)
j+8=2r+16
j=2r+16-8
j=2r+8 ....................(2)
Put the value of j from (1) to (2)
r+27=2r+8
r-2r=8-27
-r=-19
Multiply by (-1) both sides of the equation
(-1)(-r)=(-1)(-19)
r=19
Plug in the value of r in (1)
j=r+27 ............(1)
j=19+27
j=46
Present age of Jean = j = 46 years old
Present age of Rita = r = 19 years old
