Hi, Kara,
I'm not sure about my answer regarding the graph, but judge for yourself if it makes sense.
First, the equation relating how much Kiran has to spend and what he can do:
Let x and y represent the numbers of rides (x) and the number of games (y). Then let's set R for the cost per Ride, and G as the cost per Game. The total spent is given by:
Total = Rx + Gy
If the total is fixed, and the prices don't change, Kiran can choose a combination of x rides and y games as long as the total isn't exceeded. That also means that as he does more of one, he must reduce the other. (i.e., as y goes up, x must go down, and vice versa). The graph line should therefore have a negative slope (y goes down as x goes up).
Looking at the charts, I;m assuming the line represents the maximum numbers of games and rides Kiran can do with his budget. Any combination less than this line will result in money left over. Any more and he'd be in trouble.
In Graph 1, we see a line that suggests that as more games are played, more rides may be taken. This contradicts what we just concluded: if one goes up the other must go down, so this graph can't be correct. If it is, please let me know where the carnival is located and I'll be there. This is a line with a positive slope, which goes against our earlier conclusion.
A negative slope is exactly what we see in Graphs 2 and 3, but at markedly different slopes. Graph 2 says for every two games Kiran must give up 8 rides (He can do 12 rides with zero games, or 4 rides with 2 games. Wow - pretty steep trade-off. Each game is worth 4 rides. Ouch. But it is possible, if the game prizes are REALLY, REALLY good.
Graph 3 also shows the trade-off we'd expect. But now the slope isn't as steep. Now Kiran can play 8 games and only give up two rides. This is consistent, again, with the negative slop we expected.
Without any more information, I cannot legally choose between graphs 2 and 3. Both are legitimate possibilities, but I vote for Graph 3 as being the more likely to represent the situation. Why? Because no carnival would still be running if each game cost as much as 2 rides.
Please let us know what the teacher's response is. I hope this helps, and amuses,
Bob
