1. ## Euclidean Algorithm Problem

There were 63 piles of fruit put together. There are 7 different kinds of fruit. The piles were divided evenly among 23 travelers. Whats the number of fruit in each pile?

hint: consider the equation 63x + 7 = 23y

i have the equation done, 63(28) + 7 = 23(77)
but i don't exactly know what the numbers represent. My assumption is there are 207 pieces of fruit in each pile. lcm(63,23) = 1449, 1449/7 = 207. But i'm sure thats wrong. any ideas?

Hello macrobes17

Welcome to Math Help Forum!
Originally Posted by macrobes17
There were 63 piles of fruit put together. There are 7 different kinds of fruit. The piles were divided evenly among 23 travelers. Whats the number of fruit in each pile?

hint: consider the equation 63x + 7 = 23y

i have the equation done, 63(28) + 7 = 23(77)
but i don't exactly know what the numbers represent. My assumption is there are 207 pieces of fruit in each pile. lcm(63,23) = 1449, 1449/7 = 207. But i'm sure thats wrong. any ideas?
Are you sure you have given us the exact wording of the question? I can't understand the meaning of the equation $63x + 7 = 23y$.

The implication is that there were the same number of pieces of fruit in each of $63$ piles. If this number is $x$, then there were (obviously) $63x$ pieces of fruit altogether. So where does the number of different types of fruit come in? What justification is there for adding the number of different types of fruit $(7)$ to the number of pieces of fruit to give $63x + 7$? That just doesn't make any sense.

I think there must be some information that's incorrect or missing here.

3. 207 for minimum pile size is wrong. It could be 23 in which case all travelers get 63 pieces of fruit. Also in the pile that each traveler gets there will be exactly 9 of each of the 7 different fruits.

4. Originally Posted by macrobes17
There were 63 piles of fruit put together. There are 7 different kinds of fruit. The piles were divided evenly among 23 travelers. Whats the number of fruit in each pile?
hint: consider the equation 63x + 7 = 23y
i have the equation done, 63(28) + 7 = 23(77)
but i don't exactly know what the numbers represent. My assumption is there are 207 pieces of fruit in each pile. lcm(63,23) = 1449, 1449/7 = 207. But i'm sure thats wrong. any ideas?
If the 63 piles do NOT have to have the same number of each kind of fruit, then you'll need your 1449 pieces of fruit, so each traveler will get 23 pieces of fruit.
Which means that each traveler will not receive the same number of each kind of fruit.

HOWEVER,
IF each of the 63 piles contain the same number of each kind of fruit and each traveler must receive the same number of each kind of fruit then the calculation will yield something different.

Need a little clarification about the content of the piles and the distribution among the travelers.

You may need $\left( \dfrac{1449 \cdot 7}{63} = \right) 161$ pieces of fruit in each pile.
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