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12 July, 01:28

Kevin and Randy Muise have a jar containing 73? coins, all of which are either quarters or nickels. The total value of the coins in the jar is?$ 8.45. How many of each type of coin do they? have?

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  1. 12 July, 02:12
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    24 quarters and 49 nickels

    Step-by-step explanation:

    This situation has two unknowns - the total number of nickels and the total number of quarters. Because we have two unknowns, we will write a system of equations with two equations using the two unknowns.

    n+q=73 is an equation representing the total number of coins 0.05n+0.25q=8.45 is an equation representing the total value in money based on the number of coin. 0.05 and 0.25 come from the value of a nickel and quarter individually.

    We write the first equation in terms of q by subtracting it across the equal sign to get n=73-q. We now substitute this for n in the second equation.

    0.05 (73-q) + 0.25q=8.45

    3.65-0.05q+0.25q=8.45

    3.65+0.20q=8.45

    After simplifying, we subtract 3.65 across and divide by the coefficient of q.

    0.20q=4.8

    q=24

    We now know of the 73 coins that 24 are quarters. To find the number of nickels, we subtract 24 from 73 and get 49 nickels.
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