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Quadratic Applications Help (page 2)

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By — McGraw-Hill Professional
Updated on Sep 27, 2011

Quadratic Applications Practice Problems

Practice

  1. The product of two consecutive odd numbers is 399. Find the numbers.
  2. The product of two consecutive numbers is 380. Find the numbers.
  3. The product of two consecutive numbers is 650. Find the numbers.
  4. The product of two consecutive even numbers is 288. What are the numbers?
  5. Two numbers differ by 7. Their product is 228. What are the numbers?

Solution

  1. Let x = first number x + 2 = second number

    Rational Equations Solution

    There are two solutions: 19 and 21, and –21 and –19.

  2. Let x = first number x + 1 = second number

    x ( x + 1)

    = 380

    x 2 + x

    = 380

    x 2 + x – 380

    = 0

    ( x + 20)( x – 19)

    = 0

    Rational Equations Solution

    There are two solutions: 19 and 20, and –19 and –20.

  3. Let x = first number x + 1 = second number

    x ( x + 1)

    = 650

    x 2 + x

    = 650

    x 2 + x – 650

    = 0

    ( x – 25)( x + 26)

    = 0

    Rational Equations Solution

    There are two solutions: 25 and 26, and –25 and –26.

  4. Let x = first number x + 2 = second number

    x ( x + 2)

    = 288

    x 2 + 2 x

    = 288

    x 2 + 2 x – 288

    = 0

    ( x – 16)( x + 18)

    = 0

    Rational Equations Solution

    There are two solutions: 16 and 18, and –16 and –18.

  5. Let x = first number   x + 7 = second number

    x ( x + 7)

    = 228

    x 2 + 7 x

    = 228

    x 2 + 7 x – 228

    = 0

    ( x – 12)( x + 19)

    = 0

    Rational Equations Solution

    There are two solutions: 12 and 19, –12 and –19.

Practice problems for this concept can be found at: Algebra Quadratic Applications Practice Test.

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