Multiple choice

Directions: Joseph said to his daughter Eva, "Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be." If the present ages of Eva and Joseph are x and y years, respectively, represent this statement algebraically.

  1. 3x - y = -6, 7x - y = 42

  2. y - 3x = -6, 7x - y = 49

  3. 3x + y = 4, 7x + y = 42

  4. 4x - y = -1,7x - y = 4

  5. e
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A Correct answer
Explanation

Seven years ago: (y-7) = 7(x-7) => y-7 = 7x-49 => 7x-y = 42. Three years from now: (y+3) = 3(x+3) => y+3 = 3x+9 => 3x-y = -6.

AI explanation

Seven years ago, Eva and Joseph were (x - 7) and (y - 7) years old, yielding y - 7 = 7(x - 7) which simplifies to 7x - y = 42. Three years from now, their ages will be (x + 3) and (y + 3), yielding y + 3 = 3(x + 3) which simplifies to 3x - y = -6. The result is 3x - y = -6, 7x - y = 42.

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