State Quarters Gold
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AMES Gauss qn 11?
For the Pan Australian Games the three states at the top of the medals table (Victoria, S.A. and W.A) had won a total of 186 medals. Victoria has won the most gold medals and SA had as many gold medals as bronze medals. Victoria and SA won the same number of silver medals. WA had two more silver medals than bronze medals and their gold medals numbered one more than Victoria's bronze medals. Victoria had as many gold medals as the bronze medals of SA and WA combined and this number was also three quarters the total number of medals won by SA. The number of gold medals won by the three states was one less than the total number of medals won by Victoria. How many of each medal did each state win?
Got any hard ones....(joke!)
VG+SG+WG+VS+SS+WS+VB+SB+WB=186
SB=SG
VS=SS
WS=WB+2
WG=VB+1
VG=SB+WB
VG=3/4(SB+SG+SS)
VG+SG+WG=VG+VS+VB-1
8 equations in 9 unknowns.
It drops out quickly that SG=SB, SS=SB+2
I rearranged everything in terms of SB and VB and ended up with 35SB+8VB=698. There are only two solutions for this with whole numbers....VB=26, SB=14 or VB=61, SB=6. If you follow both of these through, you get to two whole number solutions, but for one of them, WG>VG which contradicts one of the criteria that Victoria had the most gold medals.
Final solution
VG=33
VS=16
VB=26
SG=14
SS=16
SB=14
WG=27
WS=21
WB=19
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A great place to shop for State Quarters Gold products is Amazon.
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