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Math Help - [SOLVED] word problem

  1. #1
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    [SOLVED] word problem

    Four boys bought a boat for $60 . The first boy paid one half of the sum of the amounts paid by the other boys. The second boy paid one third of the sum of the amounts paid by the other boys and the third boy paid one-fourth of the sum of the amounts paid by the other boys.How much did the fourth boy pay?
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  2. #2
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    Quote Originally Posted by Mr.Green View Post
    Four boys bought a boat for $60 . The first boy paid one half of the sum of the amounts paid by the other boys. The second boy paid one third of the sum of the amounts paid by the other boys and the third boy paid one-fourth of the sum of the amounts paid by the other boys.How much did the fourth boy pay?
    Ok first let's write everything down we can into equations. Let B_{1},B_{2},B_{3},B_{4} each stand for the price that each boy paid. From the first sentence, B_{1}+B_{2}+B_{3}+B_{4}=60. Now for the rest.

    "The first boy paid one half of the sum of the amounts paid by the other boys."

    B_{1}= \frac{1}{2} \left( B_{2}+B_{3}+B_{4} \right). See how that worked?

    For the second boy, it's very similar just one-third of the total of the others.

    B_{2}= \frac{1}{3} \left( B_{1}+B_{3}+B_{4} \right)

    And for the third,

    B_{3}= \frac{1}{4} \left( B_{1}+B_{2}+B_{4} \right)

    So, now we have 4 variables and 4 equations and we can solve for each of them.

    You with me so far?
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  3. #3
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    Quote Originally Posted by Jameson View Post
    Ok first let's write everything down we can into equations. Let B_{1},B_{2},B_{3},B_{4} each stand for the price that each boy paid. From the first sentence, B_{1}+B_{2}+B_{3}+B_{4}=60. Now for the rest.

    "The first boy paid one half of the sum of the amounts paid by the other boys."

    B_{1}= \frac{1}{2} \left( B_{2}+B_{3}+B_{4} \right). See how that worked?

    For the second boy, it's very similar just one-third of the total of the others.

    B_{2}= \frac{1}{3} \left( B_{1}+B_{3}+B_{4} \right)

    And for the third,

    B_{3}= \frac{1}{4} \left( B_{1}+B_{2}+B_{4} \right)

    So, now we have 4 variables and 4 equations and we can solve for each of them.

    You with me so far?
    thanks a lot to u really great help i can do the remaining steps
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  4. #4
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    You're very welcome. If you ever want to thank a poster, notice the THANKS button. Click it when you find a helpful post.
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