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23 April, 04:13

Use the 4 step process to answer this word problem: Assign and label variables, write a system of equations, solve the system, answer the question in a sentence. In your coin purse are dimes and quarters, 50 coins in all. The total value of the coins is $9.95. How many of each coin do you have?

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  1. 23 April, 06:17
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    Answer: There are 33 dimes and 17 quarters in my pocket.

    Step-by-step explanation:

    Step 1: To assign and label the variables.

    Suppose,

    The number of dimes = x

    The number of quarters = y

    Step 2: To write the system of equations.

    Equation related to the total coins:

    x + y = 50 equation 1

    Equation related to the total value of the coins:

    0.10x + 0.25y = 9.95 equation 2

    Step 3: To solve the system of equations.

    Multiply equation 1 by 0.10 and then subtract it from equation 2 to eliminate the variable, x.

    0.10x + 0.25y - (0.10x + 0.10y) = 9.95 - 5

    0.15y = 4.95

    y = 33

    So, x=50 - 33 = 17

    Step 4: Therefore, there are 33 dimes and 17 quarters in my pocket.
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