He Shoots He Scores

  • He Shoots He Scores

    PoW ID: 2908

    Algebra, High School, Algebra, Algebra, Algebra Library

    Problem Print

    When Bo got home from his basketball game last night, looking pretty pleased with himself, his roommates asked him how it went. He said that he had 10 rebounds, 2 blocks, 3 assists, and equaled or bettered his season high in points. Naturally they wanted to know exactly how many points he scored. Since he never likes to give them a straight answer, he told them the following:

    • I didn't shoot any free throws.
    • The number of 2-point baskets I made is more than twice the number of 3-point baskets I made.
    • The number of 2-pointers I made is less than or equal to 8.
    • My previous season high was 18 points.

    Now the roommates had to do some thinking! Let's see if you can figure it out.

    1. Using t to represent the number of 3-pointers he made, g to represent the number of 2-pointers, and f to represent the number of free throws, write equations or inequalities to represent all of the information given above. You should have four statements.
    2. Decide which of the four graphs below best represents the information given in the problem. Explain your choice carefully!
    3. What are all of the possible point totals for Bo?


    Graph A


    Graph B


    Graph C

    Graph D

    Answer Check

    Show Answer

    Bo might have scored 18, 19, 20, 22, 23, or 25 points.

    If your answer doesn't match ours,

    • reread the information that Bo gives his roommates and be sure that you have the right equations and inequalities.
    • check to be sure that the graph you chose agrees with the information.
    • be sure that the answers you've decided on agree with the information.
    If you think you can improve your answer, revise your solution and then leave us a comment. If you can't figure out why your answer doesn't match, tell us as much as you can in your comment and we'll try to help.

    If your answer does match our answer,

    • have you clearly answered all three questions?
    • did you explain how you decided which graph was correct?
    • are you confident that you could solve another problem like this?