Results 1 to 6 of 6
Thread: Algebra Problem

20080919, 14:22 #1
 Join Date
 Jan 2001
 Location
 La Jolla, CA
 Posts
 1,367
 Thanks
 22
 Thanked 58 Times in 54 Posts
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
 Join Date
 Nov 2001
 Location
 Melbourne, Victoria, Australia
 Posts
 5,016
 Thanks
 0
 Thanked 0 Times in 0 Posts
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
 Join Date
 Jan 2001
 Location
 La Jolla, CA
 Posts
 1,367
 Thanks
 22
 Thanked 58 Times in 54 Posts
Re: Algebra Problem
You are correct. However, did you use intuition or write the equations??

20080919, 15:05 #4
 Join Date
 Nov 2001
 Location
 Melbourne, Victoria, Australia
 Posts
 5,016
 Thanks
 0
 Thanked 0 Times in 0 Posts
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
 Join Date
 Mar 2001
 Location
 Dallas, Texas, USA
 Posts
 1,680
 Thanks
 0
 Thanked 1 Time in 1 Post
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
 Join Date
 Nov 2008
 Posts
 2
 Thanks
 0
 Thanked 0 Times in 0 Posts
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>