Ships Ahoy Math Forum Help?

[phojyt]

In a naval engagement, one-third of the fleet was captured, one- sixth was sunk, and two ships were destroyed by fire. One-seventh of the surviving ships were lost in a storm after the battle. Finally, the twenty-four remaining ships sailed home. How many ships were in the fleet before the engagement?

 

[7htas]

let the number of original ships = x

captured = x/3

sunk = x/6

destroyed by fire = 2

so number of surviving ships = x - (x/3) - (x/6) - 2



24 ships got back home

24 = 6/7 survivors

so number of surviving ships = (24/6) * 7 = 28



so x - (x/3) - (x/6) - 2 = 28

multiply both sides by 6:

6x - 2x - x - 12 = 168

3x = 180

x = 60

so 60 ships were in the original fleet

 

[sarabande]

is the second fraction 1/6th of the remaining fleet, or of the original fleet ? And the two ships sunk by fire - original fleet or part of the sequence of losses ?



I want my paper re-marked

 

[Davegriff]

48

 

[Davegriff]

second thoughts - 7htas is right - 60

 

[nattawoot]