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28 December, 07:46

We have a jar of coins, all pennies and quarters. All together, we have 302 coins, and the total value of all coins in the jar is $ 42.86. How many pennies are there in the jar?

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  1. 28 December, 10:03
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    There are 136 pennies in the jar

    Step-by-step explanation:

    The expression for the total value of money Aria has is;

    Penny has a value of = $0.01

    Quarter has a value of = $0.25

    Total value = (value of a quarter*number of quarters) + (value of a penny*number of pennies)

    where;

    Total value=$42.86

    Value of a quarter=$0.25

    number of quarters=x

    Value of a penny=0.01

    number of pennies=y

    replacing;

    42.86 = (0.25*x) + (0.01*y)

    0.25 x+0.01 y=42.86 ... equation 1

    The total number of coins=number of quarters+number of pennies

    where;

    Number of quarters=x

    Number of pennies=y

    Total number of coins=302

    replacing;

    x+y=302 ... equation 2

    Combine equation 1 and 2 and solve simultaneously;

    1 (x+y=302) 1

    -

    4 (0.25 x+0.01 y=42.86)

    x-4 (0.25 x) + y - (0.01 y*4) = 302 - (4*42.86)

    0+0.96 y=130.56

    0.96 y=130.56

    y=130.56/0.96

    y=136

    Replace the value of y in equation 2

    x+136=302

    x=302-136

    x=166

    Number of quarters=x=166

    Number of pennies=y=136
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