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Sam's coach is twice as old as Sam. When Sam started soccer 10 years ago, his coach was four times his age. How old is Sam now?

Answer 1

Kennedy Adams

#15# years ago now.

Let Sam's age be #x#. Let Sam's coach's age be #2x#.

Consequently,

#4(x-10) = 2x-10#

since #4# times the age of Sam #10# years ago was the same as the coach's #10# years ago.

Thus

#4x - 40 = 2x - 10#

#=> 2x = 30#

Therefore, Sam's age is #15#.

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Answer 2

Julia Adams

Let's denote Sam's age now as S and his coach's age as C. According to the information given, C = 2S and C - 10 = 4(S - 10). By substituting C = 2S into the second equation, we get 2S - 10 = 4S - 40. Solving this equation, we find S = 15. Therefore, Sam is currently 15 years old.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.