Changing Word Problems to Algebra
Date: 4/4/96 at 14:58:19 From: Anonymous Subject: Applications: Maximum and Minimum The difference of twice one number and three times another number is 24. Find the numbers if their product is a minimum. I've just finished a chapter on completing the square and word problems dealing with numbers, perimeters, and merchandising. So my problem is that I'm not sure if I started out right. I got 2x - 3y = 24. Is this right, and if so what next so that I can continue?
Date: 4/5/96 at 11:14:7 From: Doctor John Subject: Re: Applications: Maximum and Minimum You are on the right track. The next thing you need to do is to find an expression for the product of these two numbers. Solve the equation you have for y. You get y = (2/3)x - 8. Then it is clear that xy is can also be written as x[(2/3)x - 8]. Simplifying a little, you get (2/3)x^2 - 8x. This is a quadratic function. All you have to do now is find the minimum of the parabola that it describes. -Doctor John, The Math Forum
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