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Thread: Algebra Problem

20080919, 14:22 #1
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Algebra Problem
(since the Geometry one was so easy)
Each student in a group of 30 students studies German, Italian, or both. The total number of students studying German is three more than the total number of students studying Italian. If the number of students that study both subjects is the same as the number of students that study exactly one subject, how many students in the group study only Italian?

20080919, 14:34 #2
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Re: Algebra Problem
<span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: bold">Italian only = 6
German only = 9
Both = 15
Looks like the "trick" is to use 3 unknown variables, not just the intuitive two.</span hide>
Good problem!
Alan

20080919, 14:44 #3
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Re: Algebra Problem
You are correct. However, did you use intuition or write the equations??

20080919, 15:05 #4
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Re: Algebra Problem
I guess I intuitively wrote the equations. <img src=/S/grin.gif border=0 alt=grin width=15 height=15>
Alan

20080919, 16:34 #5
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Re: Algebra Problem
<span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: bold">01 G+I+B = 30 : <font color=yellow>German + Italian + Both = 30</font color=yellow>
02 G = I+3 : <font color=yellow>German = Italian + 3</font color=yellow>
03 B = I + I+3 : <font color=yellow>Both = Italian + Italian + 3</font color=yellow>
04 (I+3) + (I) + (I+I+3) = 30 : <font color=yellow>Substitutions for Line 01, Replace G and B with I.</font color=yellow>
05 4I + 6 = 30 : <font color=yellow>Simplify</font color=yellow>
06 4I = 24 : <font color=yellow>Subtract 6 from both sides...</font color=yellow>
07 I = 6 : <font color=yellow>Divide both sides by 4 to solve I(Italian)</font color=yellow>
08 G = 9
09 B = 15</span hide> Ricky

20081110, 09:10 #6
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Re: Algebra Problem
I used only 2 variables.
<span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: bold">Since 15 student study both, G+I=15 and then G=I+3 so I+I+3=15 </span hide>
<span style="backgroundcolor: #FFFF00; color: #FFFF00; fontweight: bold">6 students take italian</span hide>