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Math Help - High school Combination problem help?

  1. #1
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    Unhappy High school Combination problem help?

    Last year at the independent leaning center, a group of 48 students enrolled in math, french and physics. Some students were more successful than others: 32 passed french, 27 passed physics, and 33 passed math; 26 passed french and math, 26 passed physics and math, and 21 passed french math a physics. How many students passed one or more subjects?
    (6 marks for venn diagram, 2 marks for principle)


    **i don't need help with the venn diagram**


    I don't even think I am on the right track. So far I have been looking at the highest number of people who failed one subject, 21 people for physics, and subtracting it from the total number of students to get 27 people that have passed that. There are 32 people who passed french and 33 who passed math. Would 27 work because that is the lowest amount of people that could pass?



    Thank you!
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  2. #2
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    Here's what they are trying to get at. 48 people took the exam and they want to know how many people passed at least one subject. So the bare minimum would be 33, because that's how many people passed math.

    The rest of the information is to tell you how many people passed physics and french, but did not pass math. If 21 people passed all 3 subjects that means that

    33 - 21 = 12 people did not pass all 3, but passed math
    32 - 21 = 11 people did not pass all 3, but passed french
    27 - 21 = 6 people did not pass all 3, but passed physics

    if 26 people passed physics and math, that means that 1 person, out of the 27 that passed physics did not pass math. So the number of people who passed at least one subject is now 34.

    if 26 people passed french and math, that means that 6 people passed french but not math, which brings the total to 40.

    40 is the amount of people who passed at least 1 test.
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  3. #3
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    thank you so much, that really cleared things up for me.
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