contestada

Kraken and seven other pirates agreed to share a pile of gold pieces equally. Right before they divided up the gold, two more pirates showed up and demanded to be included, so the gold ended up getting divided among ten pirates instead. Kraken received 40 fewer pieces of gold than he would have if the two extra pirates hadn't arrived. How many pieces of gold did Kraken receive?

Respuesta :

aachen

When there were 8 pirates (Kraken and seven other pirates), they divided gold pieces equally. Let's assume each one got 'x' pieces. So total gold pieces were '8x'.

When two more pirates showed up and they became total 10 pirates to divide gold pieces equally. Let's assume each one got 'y' pieces. So total gold pieces were '10y'.

But the quantity of gold was same as before. It means 10y = 8x.

It also says "Kraken received 40 fewer pieces of gold than he would have if the two extra pirates hadn't arrived". It means x = 40 + y.

Substituting x = 40 + y into 10y = 8x;

10y = 8(40+y)

10y = 320 + 8y

10y - 8y = 320

2y = 320

y = 160.

Hence, Kraken received 160 pieces of gold.

Given: There are initially Kraken and 7 pirates who want to share a pile of gold equally.

Next, two other pirates i.e., Kraken and 9 other pirates want to share the gold.

The new situation leaves Kraken with 40 fewer pieces of gold than if there were only 7 other pirates except for Kraken.

To Find: The number of  pieces of gold Kraken received.

Solution:

Let x be the pieces of gold Kraken would receive in the initial situation (i.e., Kraken and 7 other pirates).

Now, in this situation, there are 8 pirates in total (including Kraken). If Kraken has received x pieces of gold, this means so have the others (since the gold would be shared equally).

This means the total amount of gold is 8x. ...(1)

In the following situation, when the two extra pirates arrive, Kraken receives 40 fewer pieces of gold than the initial sitation, i.e., Kraken's share now reduces to (x-40).

This would also be the same share as the 9 other pirates, since it's divided equally.

Over here, the total amount of gold may be written as 10(x-40). ...(2)

Since in both situations, the amount of gold remains equal, we can equate the two expressions (1) and (2)

Thus,

[tex]8x = 10(x-40)\\8x=10x -400\\2x=400\\x=200[/tex]

This means Kraken would receive 200 pieces of gold in the first situation, but with the additional two pirates arriving, Kraken's share would be (200-40)=160 pieces of gold.