SOLUTION: An island has no currency; it instead has the following exchange rate: 50 bananas = 20 coconuts 30 coconuts = 12 fish 100 fish = 1 hammock How many bananas equal 1 hammock?

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Question 10291: An island has no currency; it instead has the following exchange rate:
50 bananas = 20 coconuts
30 coconuts = 12 fish
100 fish = 1 hammock
How many bananas equal 1 hammock?
My work cannot figure this problem out.
Found 2 solutions by rapaljer, Earlsdon:
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Let's start with this:
1 hammock = 100 fish

Now remember that when you multiply 100 fish by 1, will stillhave 100 fish or 1 hammock. Also, keep in mind that when you divide two quanties that are equal to each other, you get 1. So, when you divide %2850+bananas%29%2F%2820+coconuts%29+, +%2830+coconuts%29%2F%2812+fish%29+, etc. you get 1. Right?

1 hammock = 100 fish * 1 * 1
1 hammock = 100+fish%2A+%28%2830+coconuts%29%2F%2812+fish%29%29
1 hammock = = 625 bananas!

That's a LOT of bananas!!

R^2 at SCC


Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let's rewrite the equations: For brevity, b = bananas, c = coconuts, f = fish, and h = hammock.
50b = 20c, so c = (50/20)b = (5/2)b
30c = 12f, so f = (30/12)c = (5/2)c
Now: h = 100f = 100(5/2)c = 100(5/2)(5/2)b = 100(25/4)b = (25)(25)b = 625b.
1 hammock costs 625 bananas.