13 replies to this topic

[Maggi]

You have to buy exactly 100 eggs
You have exactly 100 coins

There are 3 kinds of eggs:

A costs 7 coins for 1 egg
B costs 3 coins for 1 egg
C costs 1 coin for 3 eggs

Edit: there's one condition: you have to buy from all 3 kinds

How many eggs of each type do you need to buy in order to have spend exactly 100 coins?

Edited by Maggi, 09 November 2008 - 08:50 PM.

[Izzy]

Spoiler for Obvious unless I'm missing something...

0 of A, 0 of B, 300 of C.

[reaymond]

Spoiler for answer

25 of B and 25 of C

B = 75 coins and 25 eggs
C = 25 coins and 75 eggs

100 coins spent, and 100 eggs bought

[Maggi]

Spoiler for Obvious unless I'm missing something...

0 of A, 0 of B, 300 of C.

Uhm please read carefully, you have to buy exactly 100 eggs
Else it would have been way too easy

[reaymond]

Spoiler for Obvious unless I'm missing something...

0 of A, 0 of B, 300 of C.

But that would mean that you would buy 300 eggs. You have to buy 100 exactly

[Maggi]

Spoiler for answer

25 of B and 25 of C

B = 75 coins and 25 eggs
C = 25 coins and 75 eggs

100 coins spent, and 100 eggs bought

Sorry forgot to put the 1 condition on there, I edited it, else it would have been right though, but then it would have been very easy

[Izzy]

Oh, haha, no wonder it was so easy. I just read the last bit..

[reaymond]

A costs 7 coins for 1 egg
B costs 3 coins for 1 egg
C costs 1 coin for 3 eggs

Spoiler for ok then

buy 2 eggs from A - 14 coins and 2 egg
buy 20 eggs from B - 60 coins and 20 eggs
buy 26 eggs from C - 26 coins and 78 eggs

[Prime]

Still, there are many answers

Spoiler for All answers

x = number of 7-coin eggs
y = number of 3-coin eggs
z = number of 1/3-coin eggs

Then we have a system of two equations with three unknowns.
7x + 3y + z = 100
x + y + z = 100

The whole number solutions for (x, y, z) are:
(8 ,5, 87); (6, 10, 84); (4, 15, 81); and (2, 20,78).

[Maggi]

Still, there are many answers

Spoiler for All answers

x = number of 7-coin eggs
y = number of 3-coin eggs
z = number of 1/3-coin eggs

Then we have a system of two equations with three unknowns.
7x + 3y + z = 100
x + y + z = 100

The whole number solutions for (x, y, z) are:
(8 ,5, 87); (6, 10, 84); (4, 15, 81); and (2, 20,78).

Nice!! You found them ^^
There's only one tiny little mistake:

Spoiler for It should be

7x+3y+1/3z=100