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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

Sandra Is Twice As Old As Russell Eight Years Ago The Product Of Their Ages Was 10 Find Their Current Ages class=

Sagot :

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Eight years ago:

[tex](r - 8)(2r - 8) = 10 [/tex]

Expanding and simplifying:

[tex]2r^2 - 24r + 64 = 10 [/tex]

[tex]2r^2 - 24r + 54 = 0 [/tex]

[tex]r^2 - 12r + 27 = 0 [/tex]

Factoring the quadratic:

[tex](r - 9)(r - 3) = 0 [/tex]

Solutions:

[tex]r = 9 \quad \text{or} \quad r = 3 [/tex]

Only realistic solution:

[tex]{r = 9 }\quad \text{(ages cannot be negative)} [/tex]

Current ages:

[tex]- Russell: ( 9 ) years[/tex]

[tex]- Idra: \( 18 \) \:years[/tex]

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