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Math Help - Need Help with Equation Word Problem

  1. #1
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    Need Help with Equation Word Problem

    Hello all. Well, I received such wonderful help the first time I used this forum so I am returning with yet another equation word problem that has me stumped. When I check my work, the answer I keep coming up with is not making any sense and does not fit. Here is the problem followed by the answer I keep getting, hopefully someone will see what I am doing wrong and steer me in the right direction

    Use an equation to solve: Patricia’s bill for one year of college is $24,500. The tuition
    charge costs $4,000 more than the room and board costs. This bill also includes $500
    for fees and other charges. How much is the yearly tuition charge?

    24,500 - 4,000
    =20,500/2
    =10,250 + 500
    =10,750 (my answer)

    As you can see, this makes no sense because if you take my answer, add the room and board, the other charges and the 4,000 which gives you 1,000 too much

    10,750 + 10,250 + 500 + 4000 = 25,500
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by dclary View Post
    Hello all. Well, I received such wonderful help the first time I used this forum so I am returning with yet another equation word problem that has me stumped. When I check my work, the answer I keep coming up with is not making any sense and does not fit. Here is the problem followed by the answer I keep getting, hopefully someone will see what I am doing wrong and steer me in the right direction

    Use an equation to solve: Patricia’s bill for one year of college is $24,500. The tuition
    charge costs $4,000 more than the room and board costs. This bill also includes $500
    for fees and other charges. How much is the yearly tuition charge?

    24,500 - 4,000
    =20,500/2
    =10,250 + 500
    =10,750 (my answer)

    As you can see, this makes no sense because if you take my answer, add the room and board, the other charges and the 4,000 which gives you 1,000 too much

    10,750 + 10,250 + 500 + 4000 = 25,500
    Hi dclary,

    Let's define what we know and what we don't know.

    Let r = room and board costs

    Let r + 4000 = tuition costs (tuition is $4000 more than room and board)

    Let 500 = other costs (fees and charges)

    Let 24500 = total costs

    Now, let's add all this up to the total costs:

    r + r + 4000 + 500 = 24500

    How's that look?

    Solve for r to get room and board costs. Then add 4000 to get your tuition costs
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  3. #3
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    RE: Need Help with Equation Word Problem

    Thank you so much. If I am correctly solving for "r" the answer would be 10,000 is that correct? Thank you again for your help, I really appreciate it.
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  4. #4
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    Quote Originally Posted by dclary View Post
    Thank you so much. If I am correctly solving for "r" the answer would be 10,000 is that correct? Thank you again for your help, I really appreciate it.
    Yes, you are correct. And the tuition cost will be $4000 more than that.
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  5. #5
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    Quote Originally Posted by dclary View Post
    Hello all. Well, I received such wonderful help the first time I used this forum so I am returning with yet another equation word problem that has me stumped. When I check my work, the answer I keep coming up with is not making any sense and does not fit. Here is the problem followed by the answer I keep getting, hopefully someone will see what I am doing wrong and steer me in the right direction

    Use an equation to solve: Patricia’s bill for one year of college is $24,500. The tuition
    charge costs $4,000 more than the room and board costs. This bill also includes $500
    for fees and other charges. How much is the yearly tuition charge?

    24,500 - 4,000
    =20,500/2
    =10,250 + 500
    =10,750 (my answer)

    As you can see, this makes no sense because if you take my answer, add the room and board, the other charges and the 4,000 which gives you 1,000 too much

    10,750 + 10,250 + 500 + 4000 = 25,500
    let x be the room and board costs
    since tuition is 4000 more than room and board then the eq becomes

    x+x+4000+500=24500
    2x=20000
    x=10000

    tuition=x+4000=$14000
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