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16 May, 21:01

Andy has 31 coins made up of quarters and half dollars, and their total value is $11.00. How many quarters does he have?

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  1. 16 May, 21:27
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    4

    Step-by-step explanation:

    This situation has two unknowns - the total number of half dollars 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.

    h+q=31 is an equation representing the total number of coins 0.50h+0.25q=11 is an equation representing the total value in money based on the number of coin. 0.50 and 0.25 come from the value of a half dollar and quarter individually.

    We write the first equation in terms of q by subtracting it across the equal sign to get h=31-q. We now substitute this for h in the second equation.

    0.50 (31-q) + 0.25q=11

    15.5-0.50q+0.25q=11

    15.5-0.25q=11

    After simplifying, we subtract 15.5 across and divide by the coefficient of q.

    -0.25q=-4.5

    q=4

    We now know of the 31 coins that 4 are quarters.
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