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Gerry is 14 years old. Her mother is 38. How many years ago was the mother exactly 5 times as old as Gerry?

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[tex]8 \: years \: old[/tex]

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[tex]38 - x = 5 \times (14 - x)[/tex]

[tex]( \: Expand \: ) \: 38 - x = 70 - 5x[/tex]

[tex]( \: Simplify \: ) \: - x = - 5x + 32[/tex]

[tex]( \: Add \: 5x \: to \: both \: sides \: ) \: - x + 5x = 32[/tex]

[tex]( \: Simply \: ) \: 4x = 32[/tex]

[tex]( \: Divide \: both \: sides \: by \: 4 \: ) \: x = \frac{32}{4} [/tex]

[tex]x = 8[/tex]

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