D. LET XTHE SMALLER INTEGER AND LET YTHE LARGER INTEGER. THE FIRST...

9. d. Let xthe smaller integer and let ythe larger integer. The first sentence translates to yx7and the second sentence translates to x

²

+ y

²

169. Solve this equation by solving for yin the firstequation (yx+ 7) and substituting into the second equation.x

²

+ y

²

169x

²

+ (x+ 7)

²

169Use FOIL to multiply out (x+ 7)

²

: x

²

+ x

²

+ 7x+ 7x+ 49 169Combine like terms: 2x

²

+ 14x+ 49 169Subtract 169 from both sides: 2x

²

+ 14x+ 49169 1691692x

²

+ 14x120 0Factor the left side: 2 (x

²

+ 7x60) 02 (x+ 12)(x5) 0Set each factor equal to zeroand solve 2 0 x+ 12 0. x5 0x 12 or x5Reject the solution of12 because the integers are positive. Therefore, the larger integer is 5 + 7 12.A much easier way to solve this problem would be to look at the answer choices and find the solutionthrough trial and error.

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Q U A N T I TAT I V E P R E T E S T

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