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algebra

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A bank teller has 35 bills in $5, $10, and $20 denominations. The total value from these bills is $370.The total number of $10 bills and $20 bills is 7more than the number of $5. How many bills of each denomination?

  • algebra -

    No. of $5=bills a, $10 bill=b and $20 bill=c
    Then a+b+c=35
    5a+10b+20c=370, and
    b+c=a+7.

    Substituting value of b+c in first eq.,
    a+(a+7)=35 or 2a=28 or a=14 and
    b+c=35-14=21.
    Substituting value of a in second eq., 14x5+10b+20c=370 or 10b+20c=370-70
    Or 10b+20c=300 or b+2c=30
    Subtract from this the eq. b+c=21 and we get c=30-21=9. thus b=35-14-9=12.
    Check:14x5+12x10+9x20=370
    70+120+180=370 OK.

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