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Thread: The sum of three numbers

  1. #1
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    The sum of three numbers

    The sum of three numbers is 98. The first number is 2/3 of the second, and the second is 5/8 of the third. What is the second number?

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  2. #2
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    Hello, Amy!

    The sum of three numbers is 98.
    The first number is 2/3 of the second, and the second is 5/8 of the third.
    What is the second number?

    Let the three numbers be: $\displaystyle a,b,c.$


    "Their sum is 98": .$\displaystyle a + b + c \:=\:98$ .[1]

    "The first is 2/3 of the second": .$\displaystyle a \:=\:\frac{2}{3}b$ .[2]

    "The second is 5/8 of the third": .$\displaystyle b \:=\:\frac{5}{8}c \quad\Rightarrow\quad c \:=\:\frac{8}{5}b$ .[3]


    Substitute [2] and [3] into [1]: .$\displaystyle \frac{2}{3}b + b + \frac{8}{5}b \:=\:98$

    Multiply by 15: .$\displaystyle 10b + 15b + 24b \:=\:1470 \quad\Rightarrow\quad 49b \:=\:1470$


    . . Therefore: .$\displaystyle \boxed{b \;=\;30}$

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  3. #3
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    I do not understand how they all became b
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