SOLUTION: A fruit shop sells apples for 5 cents each, oranges for 10 cents each and bananas for 25 cents each . if you spend exactly 55 cents at the shop, how many distinct purchases of exac

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Question 293400: A fruit shop sells apples for 5 cents each, oranges for 10 cents each and bananas for 25 cents each . if you spend exactly 55 cents at the shop, how many distinct purchases of exactly two kinds of fruit can you make ?
A 7 b 8 c 9 d 14 e 18

Found 2 solutions by richwmiller, Edwin McCravy:
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
5a+10o+25b=55
2 bananas and one apple
1 banana and 3 oranges
1 banana and 6 apples
1 orange 9 apples
2 oranges 7 apples
3 oranges 5 apples
4 oranges 3 apples
5 oranges 1 apple
8 arrangements of two fruits
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!

If you don't buy any bananas, you can buy from 
1 to 5 oranges and always be able to buy apples
to finish out the 55 cents. So that's 5 ways.

If you buy 1 banana, then if you buy no apples, 
you can buy 3 oranges, or if you buy no oranges 
you can buy 6 apples.  That's 2 more ways.

If you buy 2 bananas, then you must buy 1 apple.
That's 1 more way way.

That's 8 ways, choice b 
  
Edwin
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