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Sandra is twice as old as Russell. Eight years ago, the product of their ages was 10. Find their current ages.
Let S represent Russell's current age. According to the problem:
A. Sandra is twice as old as Russell. Therefore, Sandra's current age is 2S
B. Eight years ago, the product of their ages was 10. Eight years ago, Russell's age was
S−8 and Sandra's age was 2S−8.
[tex](s−8)(2s−8)=10[/tex]
[tex]2s^{2} −8s−16s+64=10[/tex]
[tex]2s {}^{2} −24s+54=0[/tex]
[tex]s {}^{2} −12s+27[/tex]
To factorize s²-12s+27 , we look for two numbers that multiply to 27 and add up to -12. These numbers are -3 and -9
[tex](s−3)(s−9)=0[/tex]
So,
[tex]s=3 \\ or \\ s=9.[/tex]
To ascertain the correctness of both solutions, we must verify them. Sandra should be twice as old as Russell is, and the product of the ages eight years ago should be ten.
if s = 3 , Russell's current age is 3 and Sandra's current age would be 2s = 2 × 3 = 6
3−8 = − 5 (not possible since age cannot be negative) therefore this solution is not valid
If s = 9
Sandra's current age would be 2s = 2 × 9 = 18