Word problem.. Please help?

Of a group of boys and girls at camp, 22 girls leave early for a trip to the amazon. In the remaining group, there are twice as many boys as girls. But then 40 boys leave on a whitewater rafting trip, and this leaves us with three times as many girls as boys. How many boys and girls were there in the original group?

Please explain your answer for 10 points. Thanks!

3 Answers

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  • 1 decade ago
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    Let b = number of boys and g = number of girls initially.

    If 22 girls leave, there are g - 22 left, and the problem says that b is twice as many. So we have

    b = 2(g - 22)

    Then 40 boys leave, giving b - 40 remaining. Now there are three times as many girls remaining, or

    3(b - 40) = g - 22

    Substituting for b in the second equation using the first, we get

    3(2(g-22) - 40) = g-22 or after multiplyting and simplifying the left side

    6g - 252 = g - 22 which is easily solved as g = 46

    Then, subsitute 46 in the first equation for g, giving

    2 (46 - 22 ) = b or b = 48.

    As a reality check, walk through the problem and see if it works out.

  • 1 decade ago

    b = 2(g - 22), eq#1

    3(b - 40) = g - 22, eq#2

    multiply eq#2 by 2

    2*3(b - 40) = 2*(g - 22)

    6b - 240 = 2(g - 22)

    subtract eq#1

    5b - 240 = 0

    b = 240/5

    b = 48

    g = b/2 + 22

    g = 48/2 + 22

    g = 46

  • 1 decade ago

    okay, let b be number of boys and

    g be number of girls in original group,

    then

    b=2(g-22) and

    3(b-40)=g-22.

    SO, solving, you get

    b=48 and

    g=46.

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