ALgebra

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sam has $3.50 in dimes and quarters. he has 23 quarters all together. how many of each does he have?

will has $2.40 in dimes and nickels. he has 30 coins all together. how many of each does he have?

  • ALgebra -

    1. Your prob. says sam has 23qtrs,but
    I'm assuming you meant 23 coins; he can't have 23 qtrs if he only has 3.50.

    x dimes, y qtrs,
    Eq1: x + y = 23 coins,

    0.10x + 0.25y = 3.50,
    Multiply both sides by 20:
    Eq2: 2x + 5y = 70.

    Solve the 2 Eqs:
    x + y = 23,
    2x + 5y = 70,
    Multiply the 1st Eq by -2:
    -2x -2y = -46,
    2x + 5y = 70,
    Add the 2 Eqs:
    3y = 24,
    y = 8 Qtrs.

    Substitute 8 for y in EQ1:
    X + 8 = 23,
    X = 23 - 8,
    X = 15 Dimes.

    2. Same procedure as prob. 1.

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