SOLUTION: Rizza's age is one year more than Norie's age. Eight years ago, the sum of their ages was equal to Rizza's age ten years from now. How old are they now?

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Question 480473: Rizza's age is one year more than Norie's age. Eight years ago, the sum of their ages was equal to Rizza's age ten years from now. How old are they now?

Answer by mathstutor494(95) (Show Source):
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Let Norie's age : x
then Rizza's age :x+1
Eight years ago....
Norie's age : x-8
Rizza's age :x+1-8
Sum of their ages 8 years ago
(x-8)+(x+1-8)
=x-8+x+1-8
=2x-15
Also given that the sum of their ages was equal to Rizza's age ten years from now, which leads to
2x-15=x+1+10
2x-15=x+11
Transposing similar terms leads to....
2x-x=11+15
So x=26 which is Norie's age
and Rizza's age would be 26+1=27
Ans: Norie and Rizza are 26 and 27 years old now