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Mae open her coin purse and found pennies,nickels and dimes with a total value of $2.85.If there are twice as many pennies as there are nickels and dimes combined.How many pennies,dimes and nickels are there if she has a collection of 90 coins

given:
penny= 1 cent =$0.01
nickel= 5 cents =$0.05
dine= 10 cents =$0.10
quarter= 25 cents =$0.25
half= 50 cents =$0.50
dollar= 100 cents =$1

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2 answers

  1. by Reiny's formation of equations,
    eqn.1. should look like n + d + 2(n + d)=90
    3n + 3d=90
    3(n + d)=90
    n + d=30
    n=30 - d

    eqn.2. 5n + 10d + 2(n + d)=285
    7n + 12d=285
    7(30 - d) + 12 d=285
    5d= 70
    [d=15]

    then lets find out n:
    n=30-15
    [n=15]

    lets check if it all adds to 90 coins:
    n + d + 2(n + d)
    15 + 15 + 2(15 + 15)
    30 + 60
    90 coins checks out

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  2. number of nickels --- n
    number of dimes ---- d
    number of pennies --- n+d

    n + d + n+d = 90
    2n+2d = 90
    n+d = 45 or d = 45-n

    value equation:
    5n + 10d + 1(n+d) = 285
    6n + 11d = 285

    using substitution:
    6n + 11(45-n) = 285
    6n + 495 - 11n = 285
    -5n = -210
    n = 42
    d = 45-42 = 3

    so we have 42 nickels, 3 dimes and 45 pennies

    check:
    do they add up to 90 ? YEAH
    what is their value?
    42(5) + 3(10) + 45(1) = 285. YEAHHH!!!

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