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anonymous

  • 5 years ago

A basketball player averaged 20 points a game over the course of six games. His scores in five of those games were 23, 18, 16, 24, and 27. How many points did he score in the sixth game?

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  1. heisenberg
    • 5 years ago
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    So this is a basic algebra problem. Using your knowledge for averages and treating any unknown values as variables, let's take look:

  2. heisenberg
    • 5 years ago
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    the average of n numbers: (n1 + n2 + n3 + ... nn) / n ie: \[\frac{\sum_{i=1}^{n}n_i}{n}\]

  3. heisenberg
    • 5 years ago
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    that notation may be a little advanced. it just says the sum of all the numbers divided by the number of numbers. so we can carry on, treating unknowns as variables and then attempting to solve:

  4. heisenberg
    • 5 years ago
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    \[\frac{(23 + 18 + 16 + 24 + 27 + x)}{6} = 20\] now we solve for x

  5. heisenberg
    • 5 years ago
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    108 + x = 20 * 6

  6. heisenberg
    • 5 years ago
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    x = 120 - 108 = 12.

  7. heisenberg
    • 5 years ago
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    so we know in his 6th game he scored 12 points.

  8. anonymous
    • 5 years ago
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    Thank you, but how did you know to subtract? do you do the opposite when you flip the equation over

  9. heisenberg
    • 5 years ago
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    yes, when dealing with an equation, if you do one thing to one side of the equation, you must do the same to the other side. Since we had 108 + x = 20 * 6 we want to just have x on the left side, so we subtract 108 from each side. 108 + x - 108 = 20 * 6 - 108 the 108s on the left cancel, like we wanted.

  10. anonymous
    • 5 years ago
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    thank you so much,

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