Step 7 Answer the question

After working hard at solving the quadratic equation, it s tempting to just sit back, relax, and think that your work is done. Not so. The solution of the equation that you think will work is that y = 8. What is y Does its value answer the question  

y represents the distance that Shirley walked. The question asks how far Shelly walked, so the number 8 is not the answer to the question. To determine how far Shelly walked, use 2y - 1 and replace the y with 8. You get that 2(8) - 1 = 16 - 1 = 15. So Shelly walked 15 miles. 

Accuracy and common sense go hand in hand. You can t have one without the other. The accuracy part goes to the arithmetic or algebra involved in solving the problem and whether the relationships hold. The common sense refers to whether the answer — even though it s the solution of an equation — really fits the problem and the real world. 

In the case of Shirley and Shelly who walked away from each other in directions that are right angles from one another, you find that Shirley walked 8 miles and Shelly walked 15 miles. They re only 17 miles apart — even though they walked a total of 23 miles — because their journeys and the distance between them formed a right triangle. They didn t walk in opposite directions. As far as the accuracy of the solution, check out the Pythagorean theorem with the distances  

The equation checks, the answer makes sense, and the problem is solved with the question answered. 

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