Janet is 6 years younger then her brother jamie. Four years ago the product of their ages was 40. Form a quadratic equation and solve it to find the ages of the siblings.

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Let Jamie be x because Janet it defined in terms of Jamie Let Janet by x - 6 To represent their ages four years ago, subtract 4 from each expression. Jamie four years ago: x - 4 Janet four years ago: x - 6 - 4 or x - 10 The product of their ages four years ago  = 40 so (x - 4)(x - 10) = 40 x^2 -14 x + 40 = 40 x^2 -14 x = 0 x(x - 14) = 0 x cannot be 0 so x = 14 Jamie is 14 and Janet is 14 - 6 = 8