"If T+T=N+N+N+S+S=N+S+S+S and T-S=12 Find the value of S,N and T."?

i really need some help with this!!

Update:

T+T=N+N+N+S+S

T+T=N+S+S+S

N+N+N+S=N+S+S+S

T-S=12

4 Answers

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  • 1 decade ago
    Favorite Answer

    GIVEN PROBLEM:

    Find S, N and T... given...

    T+T=N+N+N+S+S=N+S+S+S .... and ... T-S=12

    ******************** *******************************

    Okay...

    T+T=N+N+N+S+S=N+S+S+S

    ..... is the same as writing ...

    2T = 3N + 2S = N + 3S

    Soo... from the rewritten simplified equation ... you can get THREE equations

    "2T = 3N + 2S = N + 3S" .... gives you...

    2T = 3N + 2S ................ (Equation #1)

    3N + 2S = N + 3S ........ (Equation #2)

    2T = N + 3S .................. (Equation #3)

    ...... and... you have the other given equation as your "4th" equation.... So....

    T - S = 12 ...................... (Equation #4)

    **************************************

    OKAY.... now let's just look at Equation 2... and rearrange it...

    3N + 2S = N + 3S

    - N ......... -N .... ( subtract "N" from both sides...)

    ---------------------

    2N + 2S = 3S

    ..... - 2S .. -2S .... ( subtract "2S" from both sides...)

    ---------------------

    2N + 0 S = S

    So we know that S = 2N... or N = S / 2

    The equations we have now are...

    2T = 3N + 2S ...... (Equation #1)

    S = 2N or N = S / 2 (Equation #2 rearranged)

    2T = N + 3S .... (Equation #3) ..... and...

    T - S = 12 ...... (Equation #4)

    Now let's look at T - S = 12.... that means that T = 12 + S, right?

    Okay... Now let's take Equation #1.... and make substitutions...

    2T = 3N + 2S (This was our original Equation #1)

    From rearranging Equation #2, we found that "N = S / 2".... and from rearranging Equation #4, we found that "T = 12 + S"

    2T = 3N + 2S (Equation #1 BEFORE substitutions)

    2( 12 + S ) = 3( S / 2 ) + 2S

    distribute the "2" and the "3"....

    (2)(12) + (2)(S) = (3/2)S + 2S

    24 + 2S = (3/2)S + (4/2)S

    24 + 2S = (7/2)S

    Multiply through by "2" so we are not dealing with fractions...

    You will then have....

    48 + 4S = 7S

    .... - 4S .. -4S ..... (subtract "4S" from both sides...)

    ---------------------

    48 + 0S = 3S

    48 = 3S

    3S = 48..... which means that S = 16

    You were given... " T - S = 12"

    You know S = 16.... so in order for T-S =12 to be true... that means that T = 28....

    T - S = 12 (before substitution)

    T - 16 = 12

    .. +16.. +16 .... (add "16" to both sides... )

    ------------------

    T + 0 = 28

    T = 28

    So ... now we know that S = 16 and T = 28. All we need to find now is N...

    Remember that we said that " N = S / 2" ???

    So if S = 16... then that means that N = 8 ... because...

    N = S / 2 = 16 / 2 = 8

    So there you have it.... S = 16, T = 28, and N = 8

    *******************************************

    ALWAYS CHECK your answers.....

    T+T=N+N+N+S+S=N+S+S+S and T-S=12

    2T = 3N + 2S = N + 3S

    2(28) = 3(8) + 2(16) = 8 + 3(16) .... Is this statement true?

    56 = 24 + 32 = 8 + 48

    56 = 56 = 56 ..... Yes.... this statement is true....

    Check T - S = 12....

    T - S = 12.... ???

    28 - 16 = 12

    12 = 12.... Yes... this is true...

  • 1 decade ago

    this is algebra problem... you know if same unknown being added then you can just write the number of the element involve in the addition right .... meaning if X+X the its two times you add the X ...so it equal with 2X....

    so first you have to simplify the equation.... 2T = 3N + 2S = N +3S ....and you have T-S =12

    using T-S=12 you will get T = 12 +S

    substitute T= 12 +S in the long equation just now

    2(12 +S) = 3N + 2S = N +3S

    24+2S = 3N + 2S = N +3S

    take out one equation on the left side

    24+2S = 3N +2S.....let N on the rigt side while take all other to the left

    24+2S-2S = 3N

    24= 3N

    24/3 = N

    so N= 8

    substitute N = 8 in another equation that not used yet ...N +3S

    so 24 + 2S = N+3S

    24 + 2S = 8 + 3S

    24 - 8 = 3S - 2S

    16 = S

    you now get S = 16.... to find T ... substitute in the T-S=12

    T-16 =12

    T=12 +16

    T =28

    ther you go....all the best

  • Rose
    Lv 4
    1 decade ago

    I'm getting these, but I'm not sure if I did it right...

    N=8

    S=16

    T=28

    Anyone back me up?

    (great job, Eyeshield)

  • 1 decade ago

    separate the equations i cant tell which is which...and resubmit your question

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