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in a group of 50 students, 28 speak english and 37 speak spanish. if five members speak neither language, how many speak both english and spanish?

i donn't understand... it says a group of 50 students but 28 + 37 is already grater than 50

  • math -

    Since 5 students speak neither English nor Spanish, we have a pool of 50-5=45 students who speak one or more of English or Spanish.

    Since 28 speak English, and 37 speak Spanish, the total number of 'official' language speakers is 28+37 = 65, 20 more than the number of students. Thus we can conclude that 20 students speak both English and Spanish, 28-20=8 speak only English, and 37-20=17 speak only Spanish. This adds up to 45, in addition to 5 who speak neither English nor Spanish.

  • math -

    The 28 and 37 counts are overlapping. People who speak both languages are double counted...

    numEnglishSpeakers + numSpanishSpeakers - numBothSpeakers + numSpeakNeither = 50

    28 + 37 - both + 5 = 50
    both = 20

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