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1. Ms.lynch has 21 coins in nickels and dimes. Their total value is $1.65. How many of each coin does she have?

2. A vending machine that takes only dimes and quarters contains 30 coins, with a total value of $4.20. How many of each coin are there?

  • math -

    this is similar to the question I answered on the question after this:

    pretend nickels=x
    dimes=y

    x+y=21 *total number of dimes and nickels is 21

    .05x+.1y=$1.65 *the value of x is .5 and the value of y is .1 so when you multiply it by the number of x and y you get $1.65

    now use elimination:
    first solve for one variable
    x+y=21
    y=-x+21

    now plug "x+21" as "y" in the other equation
    .05x+.1(-x+21)=$1.65
    .05x-.1x+2.1=1.65 *distribute
    -.05x=-.45
    x=9

    now plug 9 as x into the first equation
    x+y=21
    9+y=21
    y=12

    she has 9 nickels and 12 dimes

    check by plugging in answers into both equations:
    9+12=21 *correct
    and
    .05(9)+.1(12)=1.65 *correct


    now apply the same concept to number 2

  • math -

    22 Dimes
    8 quarters

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