Word Problem - XP Math - Forums

 XP Math - Forums Word Problem

 06-16-2008 #1 Equality Guest   Posts: n/a Word Problem I am having some trouble with this problem. I know the answer is 7. This is the problem... The radius of a large pizza is 1in. less then twice the radius of a small pizza.The difference between the areas of the pizzas is 33pi in^2.Find the radius of the large pizza. So this must be a quadratic equation. This is the part I don't get. Should it be like this... -33pi in^2 + 2r -1=0 Sorry couldn't find the symbol for pie. But would I multiply the -33 first? Or is my formula completely wrong. Or maybe putting the 33 on 2 sets of formulas. One that represents the small and one the large? Then subtracting the difference? Just need a shove in the right direction. Last edited by Equality; 06-16-2008 at 09:12 PM.. Reason: Another Thought
 06-16-2008 #2 Sillysidley Last Achievements   Join Date: Oct 2006 Posts: 822 Well, let the radius of the smaller circle be r, so the radius of the larger circle is 2r-1. We then have $(2r-1)^2-r^2=33$, since we just divided out the pi. Now, I just eyed it out and found r=4, so our answer is 7. If you can't see that, you can expand to get $4r^2-4r+1-r^2=33\rightarrow\3r^2-4r+1=33\rightarrow\3r^2-4r-32=0\rightarrow\(3r+8)(r-4)=0$, so we know r must be 4. Or, after getting $(2r-1)^2-r^2=33$, you can apply difference of squares to get $(3r-1)(r-1)=33$ and you can either make it a quadratic again, or in this case it's easy to examine factors and find r=4. __________________ .
 06-17-2008 #3 Equality Guest   Posts: n/a Ok. Thanks.You gave me more help then I wanted, but I was doing it backwards. So, if I originally left the 33pi^2 on the right and then divided out the square then I would of had the (2r-1)^2? This is where that square came from? Something like using a literal equation?We just started quadratic equations and this was the last question in my homework. Thanks a lot for your help, it is appreciated!
 06-17-2008 #4 Equality Guest   Posts: n/a One more thing is the r^2 also the result of dividing out the PI?
 06-17-2008 #5 Sillysidley Last Achievements   Join Date: Oct 2006 Posts: 822 Well, since we let the radius of the smaller circle be r so the bigger one is 2r-1, we can convert what it says to an equation: Since the difference of the areas is 33 pi, we have $(2r-1)^2\pi-r^2\pi=33\pi$, so we can divide out pi. __________________ .
 06-17-2008 #6 Equality Guest   Posts: n/a Thanks...thats what I was looking for.
 09-21-2008 #7 Scion Last Achievements   Join Date: Nov 2006 Posts: 446 how do you know the answer? __________________

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