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30 June, 05:45

Bob has 18 coins, both dimes and nickels, worth $1.45. How many of each coin does he have?

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  1. 30 June, 09:19
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    Dimes: 11, Nickels: 7

    Step-by-step explanation:

    Let's say the number of dimes ⇒ x and the number of nickels ⇒ y:

    We know the total number of coins, 18, such that we can format one equation to be:

    x + y = 18

    We also know the total cost of dimes and nickels, 1.45 dollars. Here we (in general) know that the cost of a dime is 0.1 dollars and the cost of a nickel is 0.05 dollars so that 0.1x represents the total cost of dimes if x represents any number, and 0.05y represents the total cost of nickels if y represents any number. Knowing this, let us format another equation to be:

    0.1x + 0.05y = 1.45

    So, we now have two equations:

    x + y = 18, and

    0.1x + 0.05y = 1.45

    Let's alter the first equation as such, so that x is isolated:

    x + y = 18

    x = 18 - y

    Now let's substitute the this value of x in the second equation and solve for y:

    0.1x + 0.05y = 1.45

    0.1 (18 - y) + 0.05y = 1.45

    1.8 - 0.1y + 0.05y = 1.45

    1.8 - 0.05y = 1.45

    -0.05y = - 0.35

    y = 7 nickels

    Knowing the number of nickels, substitute the value of y into the first equation:

    x + y = 18

    x + (7) = 18

    x = 11 dimes
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