Thread: CHALLENGE: Problem Solving - Possibly Simultaneous Equations

1. CHALLENGE: Problem Solving - Possibly Simultaneous Equations

Ok, this is a problem solving question involving the Olympic Games (made-up of course).

There are three states of Australia involved - Vic(toria), S.A and W.A

Here are the facts:

Overall, all states have won 186 medals (gold, silver and bronze).
Victoria won the most gold medals.
S.A had as many gold medals as bronze medals.
Vic and SA had the same amount of silver medals.
WA had two more silver medals than bronze medals.
WA had one more gold medal than Vic's bronze medals.
Victoria had as many gold medals as the bronze of SA and WA combined.
This number is 3/4 the total medals won by SA.
The number of gold won by all states is one less than the total of Vic's.

How many medals of each type did each state win?

2. _________Vic______S.A_________W.A
G_______a=b+d_____b_________e+1=d+1
S________c________c__________d+2
B_______e=d_______b___________d

a=b+d
$\displaystyle b+d=\frac{3}{4}(2b+c)$

b+e+1-1=b+d

e=d

4b+4d=6b+3c
4d=2b+3c

I set it out this way. I think I interpreted all the information correctly. There is of course one more equation: the sum of all the elements of the table should equal 186.