tag:blogger.com,1999:blog-6427940.post1903364705199936791..comments2023-12-05T07:50:19.855-05:00Comments on No Oil for Pacifists: Put it On the Money@nooil4pacifistshttp://www.blogger.com/profile/16688417615117569825noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-6427940.post-38159259632878744002008-03-02T15:45:00.000-05:002008-03-02T15:45:00.000-05:00OBH: I think your proof was more efficient than m...OBH: I think your proof was more efficient than mine. I went to public schools, and was taught thusly:<BR/><BR/> <BR/><B>W1) A bat and a ball cost $1.10 in total. <BR/><BR/>W2) The bat costs $1.00 more than the ball.<BR/><BR/>Q) How much does the ball cost?</B><BR/><BR/><BR/><I>Variables: Let L be bat; B be ball.</I><BR/><BR/><B>1)</B> T + L = 1.10 = <I>Algebraic of W1</I><BR/><BR/><B>2)</B> T = 1.00 + L = <I>Algebraic of W2</I><BR/><BR/><I>Substituting the value of T from 2 in 1</I><BR/><BR/><B>3)</B> (1.00 + L) + L = 1.10<BR/><BR/><I>Combining terms</I><BR/><BR/><B>4)</B> 2L + 1.00 = 1.10<BR/><BR/><I>Subtracting one from each side</I><BR/><BR/><B>5)</B> 2L=(1.10 - 1.00)<BR/><BR/><I>Simplifying</I><BR/><BR/><B>6)</B> 2L=0.10<BR/><BR/><I>Dividing each side by 2</I><BR/><BR/><B>7)</B> L=0.05<BR/><BR/><I>Plugging equation 7) into equation 1)</I><BR/><BR/><B>8)</B> T + 0.05 = 1.10<BR/><BR/><I>Subtracting 0.05 from each side</I><BR/><BR/><B>9)</B> T = 1.05<BR/><BR/><I>Plugging 9) into 1)</I><BR/><BR/><B>10)</B> 1.05 + L = 1.10<BR/><BR/><I>Subtract 1.05 from each side</I><BR/><BR/><B>11)</B> L = 0.05<BR/><BR/><B>THEREFORE [from 9) and 11)]:</B><BR/><BR/>The ball (L) costs $0.05; the bat (T) costs $1.05@nooil4pacifistshttps://www.blogger.com/profile/16688417615117569825noreply@blogger.comtag:blogger.com,1999:blog-6427940.post-44076351571213123402008-03-02T06:20:00.000-05:002008-03-02T06:20:00.000-05:00For those of you who want to understand how to der...For those of you who want to understand how to derive the answer, it is basic Algebra --<BR/><BR/>(*** SPOILER ***)<BR/><BR/>If <BR/>B== price of bat<BR/>and<BR/>A== price of ball<BR/><BR/>We have two pieces of info --<BR/>The bat + the ball is 110 cents (getting rid of the decimal)<BR/>Or:<BR/>B+A=110<BR/><BR/>We also know that:<BR/>The bat costs 100 cents more than the ball:<BR/>B=A+100<BR/><BR/>Now, the thing to realize is "equals" means "we can substitute it anywhere it appears" ---<BR/>so we can replace "A+100" for B anywhere it appears (there are some exceptions involving division, but they don't count here, rather obviously), so:<BR/><BR/>A+100+A=110<BR/>or<BR/>2*A+100=110<BR/>Subtract 100 from both sides:<BR/>2*A=10<BR/>so <BR/>A=5<BR/>and<BR/>B=105<BR/><BR/>See? Easy. :o)OBloodyHellhttps://www.blogger.com/profile/09992539380115488567noreply@blogger.com