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Example16

# Example16 - 23 x – 2 x 2 = 60 Rewriting this equation in...

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Example 2 The sum of twice one number and three times another number is 23 and their product is 20. Find the  numbers. First, circle what you must find—  the numbers . Let  x  stand for the number that is being multiplied by  2 and  y  stand for the number being multiplied by 3.  Now set up two equations. The sum of twice a number and three times another number is 23. x  + 3  y  = 23  Their product is 20. x y ) = 20  Rearranging the first equation gives y  = 23 – 2  x   Dividing each side of the equation by 3 gives Now, substituting the first equation into the second gives Multiplying each side of the equation by 3 gives

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Unformatted text preview: 23 x – 2 x 2 = 60 Rewriting this equation in standard quadratic form gives 2 x 2 – 23 x + 60 = 0 Solving this quadratic equation using factoring gives (2 x – 15)( x – 4) = 0 Setting each factor equal to 0 and solving gives With each x value we can find its corresponding y value. If , then or . If x = 4, then or . Therefore, this problem has two sets of solutions. The number being multiplied by 2 is , and the number being multiplied by 3 is , or the number being multiplied by 2 is 4 and the number being multiplied by 3 is 5....
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Example16 - 23 x – 2 x 2 = 60 Rewriting this equation in...

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