Math question involving mass, density, volume, and displacement?

One Response to “Math question involving mass, density, volume, and displacement?”

1. Lexi R says:

   January 29, 2011 at 4:43 pm

   density = mass / volume
   Therefore volume = mass / density

   volume 10c piece = 2.00 g / 8.902 g/ml = 0.2247 ml
   volume 15c piece = 5.00 g / 8.902 g/ml = 0.5617 ml

   combine volume of coins = volume of water displaced
   = 15.95 ml - 10.00 ml
   = 5.95 ml

   Now let number 10c pieces = a
   let number 25 c pieces = b

   a x 0.2247 ml + b x 0.5617 ml = 5.95 ml

   At this point, to do this question properly with similtaneous equations you actually need more information. You need information which would allow you to write an expression for a using only b, that you can sub back into the equation above. But you don’t have this. you should have been given the total mass of the coins as well, this would have helped, particulay seeing the hint you were given pertains to the masses.

   But you can finish by trial and error. You know that your coins must be in whole numbers.

   So first see if all coins are 25c
   5.95 / 0.5617 ml = 10.59. (not a whole number so coins are not all 25c pieces

   Now subtract the volume of 1 10 c piece and see if the rest are 25c pieces
   (5.95 - 0.2247) / 05617 = 10.19 (no, this is not right)

   Now subtract 2 10c pieces
   (5.95 - (2 x 0.2247)) / 0.5617 = 9.79 (nope, not this either)

   we continue like this untill we get to 9 10c pieces)
   (5.95 - (9 x 0.2247)) / 05617 = 6.99 (which is pretty much the whole number 7.. so this should be correct.

   We have 7 25 c pieces and 9 10 c pieces

   check the volumes
   ( 7 x 0.5617) + (9 x .2247) = 5.95 yay

   I’ll let you add up the coin values.