Question 1067256
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Opening comment....<br>
The wording is poor; we don't know for sure whether "the width is one half the length minus 11" means the width is {{{(1/2)(length)-11}}} or {{{(1/2)(length-11)}}}.<br>
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Note the formal algebraic solution, as shown by the other tutor, requires you to solve the equation {{{x^2-22x-1400=0}}} to find the answer to the problem.  You of course can always solve a quadratic equation by using the quadratic formula; but without that you have to factor that quadratic, and the factorization is not easy with the large numbers.<br>
So the formal algebra doesn't get you any closer to the solution.  If a formal algebraic solution is not required, you might as well solve the problem informally, by trial and error.<br>
You know the width is less than half the length; and you know the product of length and width is 700.  So look for two numbers with a product of 700 in which one of the numbers is 11 less than half the other.<br>
20*35  no; 20 is more than half of 35
10*70  no; 10 is less than half of 70, but it is not 11 less than half of 70
14*50  YES! 14 is less than half of 50, and 50/2-11=25-11=14<br>
ANSWER: The width and length are 14 and 50.<br>